Daily Papers

The distributed training of foundation models, particularly large language models (LLMs), demands a high level of communication. Consequently, it is highly dependent on a centralized cluster with fast and reliable interconnects. Can we conduct training on slow networks and thereby unleash the power of decentralized clusters when dealing with models exceeding 100 billion parameters? In this paper, we propose DiLoCoX, a low-communication large-scale decentralized cluster training framework. It combines Pipeline Parallelism with Dual Optimizer Policy, One-Step-Delay Overlap of Communication and Local Training, and an Adaptive Gradient Compression Scheme. This combination significantly improves the scale of parameters and the speed of model pre-training. We justify the benefits of one-step-delay overlap of communication and local training, as well as the adaptive gradient compression scheme, through a theoretical analysis of convergence. Empirically, we demonstrate that DiLoCoX is capable of pre-training a 107B foundation model over a 1Gbps network. Compared to vanilla AllReduce, DiLoCoX can achieve a 357x speedup in distributed training while maintaining negligible degradation in model convergence. To the best of our knowledge, this is the first decentralized training framework successfully applied to models with over 100 billion parameters.

Spatial VLMs have made substantial progress in geometric perception, yet complex spatial reasoning requiring multi-step inference over depth, distance, and scene relations remains challenging. Moreover, different spatial queries call for fundamentally different strategies: some are best addressed through purely linguistic, step-by-step deduction, while others require explicit 3D grounding before quantitative inference. We present Dual-Path Spatial Reasoning via Reinforcement Learning for Spatial VLMs (SR-REAL), a unified framework that equips a spatial VLM with two complementary reasoning paths: Language-Only Reasoning (LOR), which performs step-by-step linguistic deduction, and Detect-Then-Reason (DTR), which detects 3D geometric cues (e.g., centers or bounding boxes) via region tokens before explicit geometric inference. SR-REAL begins with a cold-start supervised fine-tuning stage that constructs LOR and DTR chain-of-thought supervision and exposes a region-to-3D interface, followed by RL that optimizes the policy model with accuracy and format rewards; for DTR, a discrete center-based detection reward further refines geometric alignment. Across diverse spatial benchmarks, SR-REAL significantly outperforms spatial VLM baselines: (i) a single RL-trained model supports both reasoning paths, with DTR excelling in region-aware tasks through precise 3D localization and LOR enhancing general spatial reasoning; (ii) jointly training both paths fosters mutual reinforcement; (iii) high-quality, blended cold-start data is crucial for stable RL optimization; and (iv) the model generalizes across datasets and domains without per-task tuning, demonstrating positive transfer between LOR and DTR.

Inverse reinforcement learning (IRL) is typically formulated as maximizing entropy subject to matching the distribution of expert trajectories. Classical (dual-ascent) IRL guarantees monotonic performance improvement but requires fully solving an RL problem each iteration to compute dual gradients. More recent adversarial methods avoid this cost at the expense of stability and monotonic dual improvement, by directly optimizing the primal problem and using a discriminator to provide rewards. In this work, we bridge the gap between these approaches by enabling monotonic improvement of the reward function and policy without having to fully solve an RL problem at every iteration. Our key theoretical insight is that a trust-region-optimal policy for a reward function update can be globally optimal for a smaller update in the same direction. This smaller update allows us to explicitly optimize the dual objective while only relying on a local search around the current policy. In doing so, our approach avoids the training instabilities of adversarial methods, offers monotonic performance improvement, and learns a reward function in the traditional sense of IRL--one that can be globally optimized to match expert demonstrations. Our proposed algorithm, Trust Region Inverse Reinforcement Learning (TRIRL), outperforms state-of-the-art imitation learning methods across multiple challenging tasks by a factor of 2.4x in terms of aggregate inter-quartile mean, while recovering reward functions that generalize to system dynamics shifts.

Provably efficient Model-Based Reinforcement Learning (MBRL) based on optimism or posterior sampling (PSRL) is ensured to attain the global optimality asymptotically by introducing the complexity measure of the model. However, the complexity might grow exponentially for the simplest nonlinear models, where global convergence is impossible within finite iterations. When the model suffers a large generalization error, which is quantitatively measured by the model complexity, the uncertainty can be large. The sampled model that current policy is greedily optimized upon will thus be unsettled, resulting in aggressive policy updates and over-exploration. In this work, we propose Conservative Dual Policy Optimization (CDPO) that involves a Referential Update and a Conservative Update. The policy is first optimized under a reference model, which imitates the mechanism of PSRL while offering more stability. A conservative range of randomness is guaranteed by maximizing the expectation of model value. Without harmful sampling procedures, CDPO can still achieve the same regret as PSRL. More importantly, CDPO enjoys monotonic policy improvement and global optimality simultaneously. Empirical results also validate the exploration efficiency of CDPO.

This paper presents Post-Decision Proximal Policy Optimization (PDPPO), a novel variation of the leading deep reinforcement learning method, Proximal Policy Optimization (PPO). The PDPPO state transition process is divided into two steps: a deterministic step resulting in the post-decision state and a stochastic step leading to the next state. Our approach incorporates post-decision states and dual critics to reduce the problem's dimensionality and enhance the accuracy of value function estimation. Lot-sizing is a mixed integer programming problem for which we exemplify such dynamics. The objective of lot-sizing is to optimize production, delivery fulfillment, and inventory levels in uncertain demand and cost parameters. This paper evaluates the performance of PDPPO across various environments and configurations. Notably, PDPPO with a dual critic architecture achieves nearly double the maximum reward of vanilla PPO in specific scenarios, requiring fewer episode iterations and demonstrating faster and more consistent learning across different initializations. On average, PDPPO outperforms PPO in environments with a stochastic component in the state transition. These results support the benefits of using a post-decision state. Integrating this post-decision state in the value function approximation leads to more informed and efficient learning in high-dimensional and stochastic environments.

Multimodal sarcasm detection requires resolving pragmatic incongruity across textual, acoustic, and visual cues through cross-modal reasoning. To enable robust sarcasm reasoning with foundation models, we propose SarcasmMiner, a reinforcement learning based post-training framework that resists hallucination in multimodal reasoning. We reformulate sarcasm detection as structured reasoning and adopt a dual-track distillation strategy: high-quality teacher trajectories initialize the student model, while the full set of trajectories trains a generative reward model (GenRM) to evaluate reasoning quality. The student is optimized with group relative policy optimization (GRPO) using decoupled rewards for accuracy and reasoning quality. On MUStARD++, SarcasmMiner increases F1 from 59.83% (zero-shot), 68.23% (supervised finetuning) to 70.22%. These findings suggest that reasoning-aware reward modeling enhances both performance and multimodal grounding.

Graphical User Interface (GUI) agents require effective use of historical context to perform sequential navigation tasks. While incorporating past actions and observations can improve decision making, naive use of full history leads to excessive computational overhead and distraction from irrelevant information. To address this, we introduce HiconAgent, a GUI agent trained with History Context-aware Policy Optimization (HCPO) for efficient and effective utilization of historical information. HCPO optimizes history usage in both sampling and policy updates through two complementary components: (1) Dynamic Context Sampling (DCS) presents the agent with variable length histories during sampling, enabling adaptive use of the most relevant context; (2) Anchor-guided History Compression (AHC) refines the policy update phase with a dual branch strategy where the compressed branch removes history observations while keeping history actions as information flow anchors. The compressed and uncompressed branches are coupled through a history-enhanced alignment loss to enforce consistent history usage while maintaining efficiency. Experiments on mainstream GUI navigation benchmarks demonstrate strong performance. Despite being smaller, HiconAgent-3B outperforms GUI-R1-7B by +8.46 percent grounding accuracy and +11.32 percent step success rate on GUI-Odyssey, while achieving comparable results on AndroidControl and AITW with up to 2.47x computational speedup and 60 percent FLOPs reduction.

Hallucination and factuality deficits remain key obstacles to the reliability of large language models (LLMs) in long-form generation. Existing reinforcement learning from human feedback (RLHF) frameworks primarily rely on preference rewards, yet they often overlook the model's internal knowledge boundaries, exacerbating the so-called "hallucination tax". To address this challenge, we propose Knowledge-Level Consistency Reinforcement Learning Framework (KLCF), a novel framework that focuses on the knowledge consistency between the policy model's expressed knowledge and the base model's parametric knowledge, and introduces a Dual-Fact Alignment mechanism to jointly optimize factual recall and precision. Specifically, KLCF leverages pretrained knowledge boundaries to construct fact checklist, guiding online reinforcement learning to improve factual coverage and recall; simultaneously, it trains a self-assessment module based on the base model's internal knowledge to enhance factual precision during generation. Unlike prior methods that rely on external retrieval or heavy verification, our reward design is fully external-knowledge-free and lightweight, making KLCF efficient and easily scalable to large-scale training. Experimental results demonstrate that KLCF substantially improves factuality metrics across multiple long-form benchmarks and effectively alleviates model hallucinations.

We present Datarus-R1-14B, a 14 B-parameter open-weights language model fine-tuned from Qwen 2.5-14B-Instruct to act as a virtual data analyst and graduate-level problem solver. Datarus is trained not on isolated question-answer pairs but on full analytical trajectories including reasoning steps, code execution, error traces, self-corrections, and final conclusions, all captured in a ReAct-style notebook format spanning finance, medicine, numerical analysis, and other quantitative domains. Our training pipeline combines (i) a trajectory-centric synthetic data generator that yielded 144 000 tagged notebook episodes, (ii) a dual-reward framework blending a lightweight tag-based structural signal with a Hierarchical Reward Model (HRM) that scores both single-step soundness and end-to-end coherence, and (iii) a memory-optimized implementation of Group Relative Policy Optimization (GRPO) featuring KV-cache reuse, sequential generation, and reference-model sharding. A cosine curriculum smoothly shifts emphasis from structural fidelity to semantic depth, reducing the format collapse and verbosity that often plague RL-aligned LLMs. A central design choice in Datarus is it dual reasoning interface. In agentic mode the model produces ReAct-tagged steps that invoke Python tools to execute real code; in reflection mode it outputs compact Chain-of-Thought (CoT) traces delimited by <think> and <answer> tags. On demanding postgraduate-level problems, Datarus exhibits an "AHA-moment" pattern: it sketches hypotheses, revises them once or twice, and converges avoiding the circular, token-inflating loops common to contemporary systems. Across standard public benchmarks Datarus surpasses similar size models and even reaches the level of larger reasoning models such as QwQ-32B achieving up to 30% higher accuracy on AIME 2024/2025 and LiveCodeBench while emitting 18-49% fewer tokens per solution.

The growing safety concerns surrounding large language models raise an urgent need to align them with diverse human preferences to simultaneously enhance their helpfulness and safety. A promising approach is to enforce safety constraints through Reinforcement Learning from Human Feedback (RLHF). For such constrained RLHF, typical Lagrangian-based primal-dual policy optimization methods are computationally expensive and often unstable. This paper presents a perspective of dualization that reduces constrained alignment to an equivalent unconstrained alignment problem. We do so by pre-optimizing a smooth and convex dual function that has a closed form. This shortcut eliminates the need for cumbersome primal-dual policy iterations, greatly reducing the computational burden and improving training stability. Our strategy leads to two practical algorithms in model-based and preference-based settings (MoCAN and PeCAN, respectively). A broad range of experiments demonstrate the effectiveness and merits of our algorithms.

With the widespread adoption of machine learning systems, the need to curtail their behavior has become increasingly apparent. This is evidenced by recent advancements towards developing models that satisfy robustness, safety, and fairness requirements. These requirements can be imposed (with generalization guarantees) by formulating constrained learning problems that can then be tackled by dual ascent algorithms. Yet, though these algorithms converge in objective value, even in non-convex settings, they cannot guarantee that their outcome is feasible. Doing so requires randomizing over all iterates, which is impractical in virtually any modern applications. Still, final iterates have been observed to perform well in practice. In this work, we address this gap between theory and practice by characterizing the constraint violation of Lagrangian minimizers associated with optimal dual variables, despite lack of convexity. To do this, we leverage the fact that non-convex, finite-dimensional constrained learning problems can be seen as parametrizations of convex, functional problems. Our results show that rich parametrizations effectively mitigate the issue of feasibility in dual methods, shedding light on prior empirical successes of dual learning. We illustrate our findings in fair learning tasks.

Stochastic dual dynamic programming (SDDP) is a state-of-the-art method for solving multi-stage stochastic optimization, widely used for modeling real-world process optimization tasks. Unfortunately, SDDP has a worst-case complexity that scales exponentially in the number of decision variables, which severely limits applicability to only low dimensional problems. To overcome this limitation, we extend SDDP by introducing a trainable neural model that learns to map problem instances to a piece-wise linear value function within intrinsic low-dimension space, which is architected specifically to interact with a base SDDP solver, so that can accelerate optimization performance on new instances. The proposed Neural Stochastic Dual Dynamic Programming (nu-SDDP) continually self-improves by solving successive problems. An empirical investigation demonstrates that nu-SDDP can significantly reduce problem solving cost without sacrificing solution quality over competitors such as SDDP and reinforcement learning algorithms, across a range of synthetic and real-world process optimization problems.

The goal of reinforcement learning (RL) is to find a policy that maximizes the expected cumulative return. It has been shown that this objective can be represented as an optimization problem of state-action visitation distribution under linear constraints. The dual problem of this formulation, which we refer to as dual RL, is unconstrained and easier to optimize. In this work, we first cast several state-of-the-art offline RL and offline imitation learning (IL) algorithms as instances of dual RL approaches with shared structures. Such unification allows us to identify the root cause of the shortcomings of prior methods. For offline IL, our analysis shows that prior methods are based on a restrictive coverage assumption that greatly limits their performance in practice. To fix this limitation, we propose a new discriminator-free method ReCOIL that learns to imitate from arbitrary off-policy data to obtain near-expert performance. For offline RL, our analysis frames a recent offline RL method XQL in the dual framework, and we further propose a new method f-DVL that provides alternative choices to the Gumbel regression loss that fixes the known training instability issue of XQL. The performance improvements by both of our proposed methods, ReCOIL and f-DVL, in IL and RL are validated on an extensive suite of simulated robot locomotion and manipulation tasks. Project code and details can be found at this https://hari-sikchi.github.io/dual-rl.

Constrained Markov Decision Processes (CMDPs) are critical in many high-stakes applications, where decisions must optimize cumulative rewards while strictly adhering to complex nonlinear constraints. In domains such as power systems, finance, supply chains, and precision robotics, violating these constraints can result in significant financial or societal costs. Existing Reinforcement Learning (RL) methods often struggle with sample efficiency and effectiveness in finding feasible policies for highly and strictly constrained CMDPs, limiting their applicability in these environments. Stochastic dual dynamic programming is often used in practice on convex relaxations of the original problem, but they also encounter computational challenges and loss of optimality. This paper introduces a novel approach, Two-Stage Deep Decision Rules (TS-DDR), to efficiently train parametric actor policies using Lagrangian Duality. TS-DDR is a self-supervised learning algorithm that trains general decision rules (parametric policies) using stochastic gradient descent (SGD); its forward passes solve {\em deterministic} optimization problems to find feasible policies, and its backward passes leverage duality theory to train the parametric policy with closed-form gradients. TS-DDR inherits the flexibility and computational performance of deep learning methodologies to solve CMDP problems. Applied to the Long-Term Hydrothermal Dispatch (LTHD) problem using actual power system data from Bolivia, TS-DDR is shown to enhance solution quality and to reduce computation times by several orders of magnitude when compared to current state-of-the-art methods.

Primal-dual safe RL methods commonly perform iterations between the primal update of the policy and the dual update of the Lagrange Multiplier. Such a training paradigm is highly susceptible to the error in cumulative cost estimation since this estimation serves as the key bond connecting the primal and dual update processes. We show that this problem causes significant underestimation of cost when using off-policy methods, leading to the failure to satisfy the safety constraint. To address this issue, we propose conservative policy optimization, which learns a policy in a constraint-satisfying area by considering the uncertainty in cost estimation. This improves constraint satisfaction but also potentially hinders reward maximization. We then introduce local policy convexification to help eliminate such suboptimality by gradually reducing the estimation uncertainty. We provide theoretical interpretations of the joint coupling effect of these two ingredients and further verify them by extensive experiments. Results on benchmark tasks show that our method not only achieves an asymptotic performance comparable to state-of-the-art on-policy methods while using much fewer samples, but also significantly reduces constraint violation during training. Our code is available at https://github.com/ZifanWu/CAL.

We consider the task of evaluating policies of algorithmic resource allocation through randomized controlled trials (RCTs). Such policies are tasked with optimizing the utilization of limited intervention resources, with the goal of maximizing the benefits derived. Evaluation of such allocation policies through RCTs proves difficult, notwithstanding the scale of the trial, because the individuals' outcomes are inextricably interlinked through resource constraints controlling the policy decisions. Our key contribution is to present a new estimator leveraging our proposed novel concept, that involves retrospective reshuffling of participants across experimental arms at the end of an RCT. We identify conditions under which such reassignments are permissible and can be leveraged to construct counterfactual trials, whose outcomes can be accurately ascertained, for free. We prove theoretically that such an estimator is more accurate than common estimators based on sample means -- we show that it returns an unbiased estimate and simultaneously reduces variance. We demonstrate the value of our approach through empirical experiments on synthetic, semi-synthetic as well as real case study data and show improved estimation accuracy across the board.

We present DuPO, a dual learning-based preference optimization framework that generates annotation-free feedback via a generalized duality. DuPO addresses two key limitations: Reinforcement Learning with Verifiable Rewards (RLVR)'s reliance on costly labels and applicability restricted to verifiable tasks, and traditional dual learning's restriction to strictly dual task pairs (e.g., translation and back-translation). Specifically, DuPO decomposes a primal task's input into known and unknown components, then constructs its dual task to reconstruct the unknown part using the primal output and known information (e.g., reversing math solutions to recover hidden variables), broadening applicability to non-invertible tasks. The quality of this reconstruction serves as a self-supervised reward to optimize the primal task, synergizing with LLMs' ability to instantiate both tasks via a single model. Empirically, DuPO achieves substantial gains across diverse tasks: it enhances the average translation quality by 2.13 COMET over 756 directions, boosts the mathematical reasoning accuracy by an average of 6.4 points on three challenge benchmarks, and enhances performance by 9.3 points as an inference-time reranker (trading computation for accuracy). These results position DuPO as a scalable, general, and annotation-free paradigm for LLM optimization.

Critic-free methods like GRPO reduce memory demands by estimating advantages from multiple rollouts but tend to converge slowly, as critical learning signals are diluted by an abundance of uninformative samples and tokens. To tackle this challenge, we propose the Dynamic Dual-Level Down-Sampling (D^3S) framework that prioritizes the most informative samples and tokens across groups to improve the efficient of policy optimization. D^3S operates along two levels: (1) the sample-level, which selects a subset of rollouts to maximize advantage variance (Var(A)). We theoretically proven that this selection is positively correlated with the upper bound of the policy gradient norms, yielding higher policy gradients. (2) the token-level, which prioritizes tokens with a high product of advantage magnitude and policy entropy (|A_{i,t}|times H_{i,t}), focusing updates on tokens where the policy is both uncertain and impactful. Moreover, to prevent overfitting to high-signal data, D^3S employs a dynamic down-sampling schedule inspired by curriculum learning. This schedule starts with aggressive down-sampling to accelerate early learning and gradually relaxes to promote robust generalization. Extensive experiments on Qwen2.5 and Llama3.1 demonstrate that integrating D^3S into advanced RL algorithms achieves state-of-the-art performance and generalization while requiring fewer samples and tokens across diverse reasoning benchmarks. Our code is added in the supplementary materials and will be made publicly available.

The Base-New Trade-off (BNT) problem universally exists during the optimization of CLIP-based prompt tuning, where continuous fine-tuning on base (target) classes leads to a simultaneous decrease of generalization ability on new (unseen) classes. Existing approaches attempt to regulate the prompt tuning process to balance BNT by appending constraints. However, imposed on the same target prompt, these constraints fail to fully avert the mutual exclusivity between the optimization directions for base and new. As a novel solution to this challenge, we propose the plug-and-play Dual-Prompt Collaboration (DPC) framework, the first that decoupling the optimization processes of base and new tasks at the prompt level. Specifically, we clone a learnable parallel prompt based on the backbone prompt, and introduce a variable Weighting-Decoupling framework to independently control the optimization directions of dual prompts specific to base or new tasks, thus avoiding the conflict in generalization. Meanwhile, we propose a Dynamic Hard Negative Optimizer, utilizing dual prompts to construct a more challenging optimization task on base classes for enhancement. For interpretability, we prove the feature channel invariance of the prompt vector during the optimization process, providing theoretical support for the Weighting-Decoupling of DPC. Extensive experiments on multiple backbones demonstrate that DPC can significantly improve base performance without introducing any external knowledge beyond the base classes, while maintaining generalization to new classes. Code is available at: https://github.com/JREion/DPC.

We consider function optimization as a sequential decision making problem under budget constraint. This constraint limits the number of objective function evaluations allowed during the optimization. We consider an algorithm inspired by a continuous version of a multi-armed bandit problem which attacks this optimization problem by solving the tradeoff between exploration (initial quasi-uniform search of the ___domain) and exploitation (local optimization around the potentially global maxima). We introduce the so-called Simultaneous Optimistic Optimization (SOO), a deterministic algorithm that works by ___domain partitioning. The benefit of such approach are the guarantees on the returned solution and the numerical efficiency of the algorithm. We present this machine learning approach to optimization, and provide the empirical assessment of SOO on the CEC'2014 competition on single objective real-parameter numerical optimization test-suite.

Multi-objective reinforcement learning (MORL) seeks to learn policies that balance multiple, often conflicting objectives. Although a single preference-conditioned policy is the most flexible and scalable solution, existing approaches remain brittle in practice, frequently failing to recover complete Pareto fronts. We show that this failure stems from two structural issues in current methods: destructive gradient interference caused by premature scalarization and representational collapse across the preference space. We introduce D^3PO, a PPO-based framework that reorganizes multi-objective policy optimization to address these issues directly. D^3PO preserves per-objective learning signals through a decomposed optimization pipeline and integrates preferences only after stabilization, enabling reliable credit assignment. In addition, a scaled diversity regularizer enforces sensitivity of policy behavior to preference changes, preventing collapse. Across standard MORL benchmarks, including high-dimensional and many-objective control tasks, D^3PO consistently discovers broader and higher-quality Pareto fronts than prior single- and multi-policy methods, matching or exceeding state-of-the-art hypervolume and expected utility while using a single deployable policy.

In recent years, Reinforcement Learning (RL) has been applied to real-world problems with increasing success. Such applications often require to put constraints on the agent's behavior. Existing algorithms for constrained RL (CRL) rely on gradient descent-ascent, but this approach comes with a caveat. While these algorithms are guaranteed to converge on average, they do not guarantee last-iterate convergence, i.e., the current policy of the agent may never converge to the optimal solution. In practice, it is often observed that the policy alternates between satisfying the constraints and maximizing the reward, rarely accomplishing both objectives simultaneously. Here, we address this problem by introducing Reinforcement Learning with Optimistic Ascent-Descent (ReLOAD), a principled CRL method with guaranteed last-iterate convergence. We demonstrate its empirical effectiveness on a wide variety of CRL problems including discrete MDPs and continuous control. In the process we establish a benchmark of challenging CRL problems.

Deep learning classifiers face significant challenges when dealing with heterogeneous multi-modal and multi-organ biomedical datasets. The low-level feature distinguishability limited to imaging-modality hinders the classifiers' ability to learn high-level semantic relationships, resulting in sub-optimal performance. To address this issue, image augmentation strategies are employed as regularization techniques. While additive noise input during network training is a well-established augmentation as regularization method, modern pipelines often favor more robust techniques such as dropout and weight decay. This preference stems from the observation that combining these established techniques with noise input can adversely affect model performance. In this study, we propose a novel pretraining pipeline that learns to generate conditional noise mask specifically tailored to improve performance on multi-modal and multi-organ datasets. As a reinforcement learning algorithm, our approach employs a dual-component system comprising a very light-weight policy network that learns to sample conditional noise using a differentiable beta distribution as well as a classifier network. The policy network is trained using the reinforce algorithm to generate image-specific noise masks that regularize the classifier during pretraining. A key aspect is that the policy network's role is limited to obtaining an intermediate (or heated) model before fine-tuning. During inference, the policy network is omitted, allowing direct comparison between the baseline and noise-regularized models. We conducted experiments and related analyses on RadImageNet datasets. Results demonstrate that fine-tuning the intermediate models consistently outperforms conventional training algorithms on both classification and generalization to unseen concept tasks.

Online allocation problems with resource constraints are central problems in revenue management and online advertising. In these problems, requests arrive sequentially during a finite horizon and, for each request, a decision maker needs to choose an action that consumes a certain amount of resources and generates reward. The objective is to maximize cumulative rewards subject to a constraint on the total consumption of resources. In this paper, we consider a data-driven setting in which the reward and resource consumption of each request are generated using an input model that is unknown to the decision maker. We design a general class of algorithms that attain good performance in various input models without knowing which type of input they are facing. In particular, our algorithms are asymptotically optimal under independent and identically distributed inputs as well as various non-stationary stochastic input models, and they attain an asymptotically optimal fixed competitive ratio when the input is adversarial. Our algorithms operate in the Lagrangian dual space: they maintain a dual multiplier for each resource that is updated using online mirror descent. By choosing the reference function accordingly, we recover the dual sub-gradient descent and dual multiplicative weights update algorithm. The resulting algorithms are simple, fast, and do not require convexity in the revenue function, consumption function and action space, in contrast to existing methods for online allocation problems. We discuss applications to network revenue management, online bidding in repeated auctions with budget constraints, online proportional matching with high entropy, and personalized assortment optimization with limited inventory.

Dynamic programming (DP) is a fundamental method in operations research, but formulating DP models has traditionally required expert knowledge of both the problem context and DP techniques. Large Language Models (LLMs) offer the potential to automate this process. However, DP problems pose unique challenges due to their inherently stochastic transitions and the limited availability of training data. These factors make it difficult to directly apply existing LLM-based models or frameworks developed for other optimization problems, such as linear or integer programming. We introduce DP-Bench, the first benchmark covering a wide range of textbook-level DP problems to enable systematic evaluation. We present Dynamic Programming Language Model (DPLM), a 7B-parameter specialized model that achieves performance comparable to state-of-the-art LLMs like OpenAI's o1 and DeepSeek-R1, and surpasses them on hard problems. Central to DPLM's effectiveness is DualReflect, our novel synthetic data generation pipeline, designed to scale up training data from a limited set of initial examples. DualReflect combines forward generation for diversity and backward generation for reliability. Our results reveal a key insight: backward generation is favored in low-data regimes for its strong correctness guarantees, while forward generation, though lacking such guarantees, becomes increasingly valuable at scale for introducing diverse formulations. This trade-off highlights the complementary strengths of both approaches and the importance of combining them.

While scaling individual Large Language Models (LLMs) has delivered remarkable progress, the next frontier lies in scaling collaboration through multi-agent systems (MAS). However, purely autonomous MAS remain ''closed-world'' systems, constrained by the static knowledge horizon of pre-trained models. This limitation makes them brittle on tasks requiring knowledge beyond training data, often leading to collective failure under novel challenges. To address this, we propose the Human-In-the-Loop Multi-Agent Collaboration (HILA) framework, a principled paradigm for human--agent collaboration. HILA trains agents to learn a metacognitive policy that governs when to solve problems autonomously and when to defer to a human expert. To operationalize this policy, we introduce Dual-Loop Policy Optimization, which disentangles immediate decision-making from long-term capability growth. The inner loop applies Group Relative Policy Optimization (GRPO) with a cost-aware reward to optimize deferral decisions, while the outer loop implements continual learning, transforming expert feedback into high-quality supervised signals that strengthen the agent's reasoning ability. Experiments on challenging mathematical and problem-solving benchmarks show that HILA, equipped with Dual-Loop Policy Optimization, consistently outperforms advanced MAS, establishing a principled foundation for collaborative and continually improving agentic systems.

Aligning generative models with human preference via RLHF typically suffers from overoptimization, where an imperfectly learned reward model can misguide the generative model to output undesired responses. We investigate this problem in a principled manner by identifying the source of the misalignment as a form of distributional shift and uncertainty in learning human preferences. To mitigate overoptimization, we first propose a theoretical algorithm that chooses the best policy for an adversarially chosen reward model; one that simultaneously minimizes the maximum likelihood estimation of the loss and a reward penalty term. Here, the reward penalty term is introduced to prevent the policy from choosing actions with spurious high proxy rewards, resulting in provable sample efficiency of the algorithm under a partial coverage style condition. Moving from theory to practice, the proposed algorithm further enjoys an equivalent but surprisingly easy-to-implement reformulation. Using the equivalence between reward models and the corresponding optimal policy, the algorithm features a simple objective that combines: (i) a preference optimization loss that directly aligns the policy with human preference, and (ii) a supervised learning loss that explicitly imitates the policy with a (suitable) baseline distribution. In the context of aligning large language models (LLM), this objective fuses the direct preference optimization (DPO) loss with the supervised fune-tuning (SFT) loss to help mitigate the overoptimization towards undesired responses, for which we name the algorithm Regularized Preference Optimization (RPO). Experiments of aligning LLMs demonstrate the improved performance of RPO compared with DPO baselines. Our work sheds light on the interplay between preference optimization and SFT in tuning LLMs with both theoretical guarantees and empirical evidence.

Recent advances in large vision-language models (LVLMs) have shown promise for embodied task planning, yet they struggle with fundamental challenges like dependency constraints and efficiency. Existing approaches either solely optimize action selection or leverage world models during inference, overlooking the benefits of learning to model the world as a way to enhance planning capabilities. We propose Dual Preference Optimization (D^2PO), a new learning framework that jointly optimizes state prediction and action selection through preference learning, enabling LVLMs to understand environment dynamics for better planning. To automatically collect trajectories and stepwise preference data without human annotation, we introduce a tree search mechanism for extensive exploration via trial-and-error. Extensive experiments on VoTa-Bench demonstrate that our D^2PO-based method significantly outperforms existing methods and GPT-4o when applied to Qwen2-VL (7B), LLaVA-1.6 (7B), and LLaMA-3.2 (11B), achieving superior task success rates with more efficient execution paths.

This paper presents Dual Lagrangian Learning (DLL), a principled learning methodology for dual conic optimization proxies. DLL leverages conic duality and the representation power of ML models to provide high-duality, dual-feasible solutions, and therefore valid Lagrangian dual bounds, for linear and nonlinear conic optimization problems. The paper introduces a systematic dual completion procedure, differentiable conic projection layers, and a self-supervised learning framework based on Lagrangian duality. It also provides closed-form dual completion formulae for broad classes of conic problems, which eliminate the need for costly implicit layers. The effectiveness of DLL is demonstrated on linear and nonlinear conic optimization problems. The proposed methodology significantly outperforms a state-of-the-art learning-based method, and achieves 1000x speedups over commercial interior-point solvers with optimality gaps under 0.5\% on average.

Reinforcement learning from human feedback (RLHF) methods are emerging as a way to fine-tune diffusion models (DMs) for visual generation. However, commonly used on-policy strategies are limited by the generalization capability of the reward model, while off-policy approaches require large amounts of difficult-to-obtain paired human-annotated data, particularly in visual generation tasks. To address the limitations of both on- and off-policy RLHF, we propose a preference optimization method that aligns DMs with preferences without relying on reward models or paired human-annotated data. Specifically, we introduce a Semi-Policy Preference Optimization (SePPO) method. SePPO leverages previous checkpoints as reference models while using them to generate on-policy reference samples, which replace "losing images" in preference pairs. This approach allows us to optimize using only off-policy "winning images." Furthermore, we design a strategy for reference model selection that expands the exploration in the policy space. Notably, we do not simply treat reference samples as negative examples for learning. Instead, we design an anchor-based criterion to assess whether the reference samples are likely to be winning or losing images, allowing the model to selectively learn from the generated reference samples. This approach mitigates performance degradation caused by the uncertainty in reference sample quality. We validate SePPO across both text-to-image and text-to-video benchmarks. SePPO surpasses all previous approaches on the text-to-image benchmarks and also demonstrates outstanding performance on the text-to-video benchmarks. Code will be released in https://github.com/DwanZhang-AI/SePPO.

Reinforcement learning from human feedback (RLHF) is a promising solution to align large language models (LLMs) more closely with human values. Off-policy preference optimization, where the preference data is obtained from other models, is widely adopted due to its cost efficiency and scalability. However, off-policy preference optimization often suffers from a distributional gap between the policy used for data collection and the target policy, leading to suboptimal optimization. In this paper, we propose a novel strategy to mitigate this problem by simulating on-policy learning with off-policy preference data. Our Weighted Preference Optimization (WPO) method adapts off-policy data to resemble on-policy data more closely by reweighting preference pairs according to their probability under the current policy. This method not only addresses the distributional gap problem but also enhances the optimization process without incurring additional costs. We validate our method on instruction following benchmarks including Alpaca Eval 2 and MT-bench. WPO not only outperforms Direct Preference Optimization (DPO) by up to 5.6% on Alpaca Eval 2 but also establishes a remarkable length-controlled winning rate against GPT-4-turbo of 48.6% based on Llama-3-8B-Instruct, making it the strongest 8B model on the leaderboard. We will release the code and models at https://github.com/wzhouad/WPO.

Multi-objective reinforcement learning (MORL) excels at handling rapidly changing preferences in tasks that involve multiple criteria, even for unseen preferences. However, previous dominating MORL methods typically generate a fixed policy set or preference-conditioned policy through multiple training iterations exclusively for sampled preference vectors, and cannot ensure the efficient discovery of the Pareto front. Furthermore, integrating preferences into the input of policy or value functions presents scalability challenges, in particular as the dimension of the state and preference space grow, which can complicate the learning process and hinder the algorithm's performance on more complex tasks. To address these issues, we propose a two-stage Pareto front discovery algorithm called Constrained MORL (C-MORL), which serves as a seamless bridge between constrained policy optimization and MORL. Concretely, a set of policies is trained in parallel in the initialization stage, with each optimized towards its individual preference over the multiple objectives. Then, to fill the remaining vacancies in the Pareto front, the constrained optimization steps are employed to maximize one objective while constraining the other objectives to exceed a predefined threshold. Empirically, compared to recent advancements in MORL methods, our algorithm achieves more consistent and superior performances in terms of hypervolume, expected utility, and sparsity on both discrete and continuous control tasks, especially with numerous objectives (up to nine objectives in our experiments).

Large language models (LLMs) are commonly aligned with human preferences using reinforcement learning from human feedback (RLHF). In this method, LLM policies are generally optimized through reward maximization with Kullback-Leibler (KL) divergence regularization of the reference policy. However, KL and its f-divergence variants only compare token probabilities at identical indices, failing to capture semantic similarity. We propose Wasserstein Policy Regularization (WPR), a semantic-aware regularization for the RLHF framework based on the entropy-regularized Wasserstein distance, which incorporates the geometry of the token space. The dual formulation of the distance expresses the regularization as penalty terms applied to the reward via optimal dual variables, which yield a tractable objective compatible with standard RL algorithms. Empirically, our method outperforms KL- and f-divergence-based baselines, demonstrating the benefits of semantic-aware policy distances for alignment. Our code is available at https://github.com/aailab-kaist/WPR.

When applying offline reinforcement learning (RL) in healthcare scenarios, the out-of-distribution (OOD) issues pose significant risks, as inappropriate generalization beyond clinical expertise can result in potentially harmful recommendations. While existing methods like conservative Q-learning (CQL) attempt to address the OOD issue, their effectiveness is limited by only constraining action selection by suppressing uncertain actions. This action-only regularization imitates clinician actions that prioritize short-term rewards, but it fails to regulate downstream state trajectories, thereby limiting the discovery of improved long-term treatment strategies. To safely improve policy beyond clinician recommendations while ensuring that state-action trajectories remain in-distribution, we propose Offline Guarded Safe Reinforcement Learning (OGSRL), a theoretically grounded model-based offline RL framework. OGSRL introduces a novel dual constraint mechanism for improving policy with reliability and safety. First, the OOD guardian is established to specify clinically validated regions for safe policy exploration. By constraining optimization within these regions, it enables the reliable exploration of treatment strategies that outperform clinician behavior by leveraging the full patient state history, without drifting into unsupported state-action trajectories. Second, we introduce a safety cost constraint that encodes medical knowledge about physiological safety boundaries, providing ___domain-specific safeguards even in areas where training data might contain potentially unsafe interventions. Notably, we provide theoretical guarantees on safety and near-optimality: policies that satisfy these constraints remain in safe and reliable regions and achieve performance close to the best possible policy supported by the data.

Teaching large language models (LLMs) to be faithful in the provided context is crucial for building reliable information-seeking systems. Therefore, we propose a systematic framework, CANOE, to improve the faithfulness of LLMs in both short-form and long-form generation tasks without human annotations. Specifically, we first synthesize short-form question-answering (QA) data with four diverse tasks to construct high-quality and easily verifiable training data without human annotation. Also, we propose Dual-GRPO, a rule-based reinforcement learning method that includes three tailored rule-based rewards derived from synthesized short-form QA data, while simultaneously optimizing both short-form and long-form response generation. Notably, Dual-GRPO eliminates the need to manually label preference data to train reward models and avoids over-optimizing short-form generation when relying only on the synthesized short-form QA data. Experimental results show that CANOE greatly improves the faithfulness of LLMs across 11 different downstream tasks, even outperforming the most advanced LLMs, e.g., GPT-4o and OpenAI o1.

Direct Preference Optimization (DPO) has emerged as a popular alternative to Reinforcement Learning from Human Feedback (RLHF), offering theoretical equivalence with simpler implementation. We prove this equivalence is conditional rather than universal, depending on an implicit assumption frequently violated in practice: the RLHF-optimal policy must prefer human-preferred responses. When this assumption fails, DPO optimizes relative advantage over the reference policy rather than absolute alignment with human preferences, leading to pathological convergence where policies decrease DPO loss while preferring dispreferred responses. We characterize when this assumption is violated, show the existence of an undesirable solution space, and prove that DPO and RLHF optimize fundamentally different objectives in such cases. To address this, we introduce Constrained Preference Optimization (CPO), augmenting RLHF with constraints for provable alignment. We further provide a geometric interpretation through soft margin ranking, revealing that DPO implements margin ranking with potentially negative targets. Our theoretical analysis establishes when DPOs' guarantees hold and provides solutions preserving simplicity with provable alignment. Comprehensive experiments on standard benchmarks demonstrate that CPO achieves state-of-the-art performance. Code is available at: https://github.com/visitworld123/CPO.

Policy optimization methods are powerful algorithms in Reinforcement Learning (RL) for their flexibility to deal with policy parameterization and ability to handle model misspecification. However, these methods usually suffer from slow convergence rates and poor sample complexity. Hence it is important to design provably sample efficient algorithms for policy optimization. Yet, recent advances for this problems have only been successful in tabular and linear setting, whose benign structures cannot be generalized to non-linearly parameterized policies. In this paper, we address this problem by leveraging recent advances in value-based algorithms, including bounded eluder-dimension and online sensitivity sampling, to design a low-switching sample-efficient policy optimization algorithm, LPO, with general non-linear function approximation. We show that, our algorithm obtains an varepsilon-optimal policy with only O(text{poly(d)}{varepsilon^3}) samples, where varepsilon is the suboptimality gap and d is a complexity measure of the function class approximating the policy. This drastically improves previously best-known sample bound for policy optimization algorithms, O(text{poly(d)}{varepsilon^8}). Moreover, we empirically test our theory with deep neural nets to show the benefits of the theoretical inspiration.

In RL, given a prompt, we sample a group of completions from a model and score them. Two questions follow: which completions should gain probability mass, and how should the parameters move to realize that change? Standard policy-gradient methods answer both at once, so the update can overshoot or undershoot depending on the learning rate, clipping, and other optimizer choices. We introduce Target Policy Optimization (TPO), which separates the two questions. Given scored completions, TPO constructs a target distribution q_i propto p_i^{,old} exp(u_i) and fits the policy to it by cross-entropy. The loss gradient on sampled-completion logits is p^θ- q, which vanishes once the policy matches the target. On tabular bandits, transformer sequence tasks, and billion-parameter LLM RLVR, TPO matches PG, PPO, GRPO, and DG on easy tasks and substantially outperforms them under sparse reward. Code is available at https://github.com/JeanKaddour/tpo.

Reinforcement learning has become a cornerstone technique for developing reasoning models in complex tasks, ranging from mathematical problem-solving to imaginary reasoning. The optimization of these models typically relies on policy gradient methods, whose efficacy hinges on the accurate estimation of an advantage function. However, prevailing methods typically employ static advantage estimation, a practice that leads to inefficient credit assignment by neglecting the dynamic utility of training samples over time. This limitation results in suboptimal policy updates, which in turn manifest as slower convergence rates and increased learning instability, as models fail to adapt to evolving sample utilities effectively. To address this problem, we introduce ADORA (Advantage Dynamics via Online Rollout Adaptation), a novel framework for policy optimization. ADORA dynamically adjusts the advantage function's weighting by adaptively categorizing training data into temporarily advantageous and disadvantageous samples, based on their evolving utility during online model rollouts. This tailored data differentiation strategy allows ADORA to be seamlessly integrated into existing policy optimization algorithms without significant architectural modifications, enabling the policy to prioritize learning from more informative experiences and thereby achieve more efficient policy updates. Extensive evaluations across diverse model families and varying data scales demonstrate that ADORA is a robust and efficient framework. It significantly enhances long reasoning in both geometric and mathematical tasks, consistently achieving notable performance gains without requiring sensitive hyperparameter tuning.

We introduce the framework of performative reinforcement learning where the policy chosen by the learner affects the underlying reward and transition dynamics of the environment. Following the recent literature on performative prediction~Perdomo et. al., 2020, we introduce the concept of performatively stable policy. We then consider a regularized version of the reinforcement learning problem and show that repeatedly optimizing this objective converges to a performatively stable policy under reasonable assumptions on the transition dynamics. Our proof utilizes the dual perspective of the reinforcement learning problem and may be of independent interest in analyzing the convergence of other algorithms with decision-dependent environments. We then extend our results for the setting where the learner just performs gradient ascent steps instead of fully optimizing the objective, and for the setting where the learner has access to a finite number of trajectories from the changed environment. For both settings, we leverage the dual formulation of performative reinforcement learning and establish convergence to a stable solution. Finally, through extensive experiments on a grid-world environment, we demonstrate the dependence of convergence on various parameters e.g. regularization, smoothness, and the number of samples.

The bandits with knapsack (BwK) framework models online decision-making problems in which an agent makes a sequence of decisions subject to resource consumption constraints. The traditional model assumes that each action consumes a non-negative amount of resources and the process ends when the initial budgets are fully depleted. We study a natural generalization of the BwK framework which allows non-monotonic resource utilization, i.e., resources can be replenished by a positive amount. We propose a best-of-both-worlds primal-dual template that can handle any online learning problem with replenishment for which a suitable primal regret minimizer exists. In particular, we provide the first positive results for the case of adversarial inputs by showing that our framework guarantees a constant competitive ratio alpha when B=Omega(T) or when the possible per-round replenishment is a positive constant. Moreover, under a stochastic input model, our algorithm yields an instance-independent O(T^{1/2}) regret bound which complements existing instance-dependent bounds for the same setting. Finally, we provide applications of our framework to some economic problems of practical relevance.

Diffusion policy sampling enables reinforcement learning (RL) to represent multimodal action distributions beyond suboptimal unimodal Gaussian policies. However, existing diffusion-based RL methods primarily focus on offline settings for reward maximization, with limited consideration of safety in online settings. To address this gap, we propose Augmented Lagrangian-Guided Diffusion (ALGD), a novel algorithm for off-policy safe RL. By revisiting optimization theory and energy-based model, we show that the instability of primal-dual methods arises from the non-convex Lagrangian landscape. In diffusion-based safe RL, the Lagrangian can be interpreted as an energy function guiding the denoising dynamics. Counterintuitively, direct usage destabilizes both policy generation and training. ALGD resolves this issue by introducing an augmented Lagrangian that locally convexifies the energy landscape, yielding a stabilized policy generation and training process without altering the distribution of the optimal policy. Theoretical analysis and extensive experiments demonstrate that ALGD is both theoretically grounded and empirically effective, achieving strong and stable performance across diverse environments.

Large language models enable agents to autonomously perform tasks in open web environments. However, as hidden threats within the web evolve, web agents face the challenge of balancing task performance with emerging risks during long-sequence operations. Although this challenge is critical, current research remains limited to single-objective optimization or single-turn scenarios, lacking the capability for collaborative optimization of both safety and utility in web environments. To address this gap, we propose HarmonyGuard, a multi-agent collaborative framework that leverages policy enhancement and objective optimization to jointly improve both utility and safety. HarmonyGuard features a multi-agent architecture characterized by two fundamental capabilities: (1) Adaptive Policy Enhancement: We introduce the Policy Agent within HarmonyGuard, which automatically extracts and maintains structured security policies from unstructured external documents, while continuously updating policies in response to evolving threats. (2) Dual-Objective Optimization: Based on the dual objectives of safety and utility, the Utility Agent integrated within HarmonyGuard performs the Markovian real-time reasoning to evaluate the objectives and utilizes metacognitive capabilities for their optimization. Extensive evaluations on multiple benchmarks show that HarmonyGuard improves policy compliance by up to 38% and task completion by up to 20% over existing baselines, while achieving over 90% policy compliance across all tasks. Our project is available here: https://github.com/YurunChen/HarmonyGuard.

This paper studies post-training large language models (LLMs) using preference feedback from a powerful oracle to help a model iteratively improve over itself. The typical approach for post-training LLMs involves Reinforcement Learning from Human Feedback (RLHF), which traditionally separates reward learning and subsequent policy optimization. However, such a reward maximization approach is limited by the nature of "point-wise" rewards (such as Bradley-Terry model), which fails to express complex intransitive or cyclic preference relations. While advances on RLHF show reward learning and policy optimization can be merged into a single contrastive objective for stability, they yet still remain tethered to the reward maximization framework. Recently, a new wave of research sidesteps the reward maximization presumptions in favor of directly optimizing over "pair-wise" or general preferences. In this paper, we introduce Direct Nash Optimization (DNO), a provable and scalable algorithm that marries the simplicity and stability of contrastive learning with theoretical generality from optimizing general preferences. Because DNO is a batched on-policy algorithm using a regression-based objective, its implementation is straightforward and efficient. Moreover, DNO enjoys monotonic improvement across iterations that help it improve even over a strong teacher (such as GPT-4). In our experiments, a resulting 7B parameter Orca-2.5 model aligned by DNO achieves the state-of-the-art win-rate against GPT-4-Turbo of 33% on AlpacaEval 2.0 (even after controlling for response length), an absolute gain of 26% (7% to 33%) over the initializing model. It outperforms models with far more parameters, including Mistral Large, Self-Rewarding LM (70B parameters), and older versions of GPT-4.

Direct Preference Optimization (DPO) is an effective technique that leverages pairwise preference data (usually one chosen and rejected response pair per user prompt) to align LLMs to human preferences. In practice, multiple responses can exist for a given prompt with varying quality relative to each other. With availability of such quality ratings for multiple responses, we propose utilizing these responses to create multiple preference pairs for a given prompt. Our work focuses on systematically using the constructed multiple preference pair in DPO training via curriculum learning methodology. In particular, we order these multiple pairs of preference data from easy to hard (emulating curriculum training) according to various criteria. We show detailed comparisons of our proposed approach to the standard single-pair DPO setting. Our method, which we call Curry-DPO consistently shows increased performance gains on MTbench, Vicuna, WizardLM, and the UltraFeedback test set, highlighting its effectiveness. More specifically, Curry-DPO achieves a score of 7.43 on MT-bench with Zephy-7B model outperforming majority of existing LLMs with similar parameter size. Curry-DPO also achieves the highest adjusted win rates on Vicuna, WizardLM, and UltraFeedback test datasets (90.7%, 87.1%, and 87.9% respectively) in our experiments, with notable gains of upto 7.5% when compared to standard DPO technique.

We introduce ORPO-Distill, a general-purpose method for cross-architecture LLM distillation that formulates the problem as a preference optimization task. Unlike standard CoT distillation, the approach transfers knowledge through diverse reasoning traces. It employs an Odds-Ratio Preference Optimization objective that contrasts teacher and student traces for more effective learning, and adopts a mixed-policy strategy for utilizing student-generated outputs, outperforming both off- and on-policy alternatives. Experiments on five datasets and multiple student models show consistent improvements over conventional black-box KD baselines.

Robust Markov decision processes (RMDPs) provide a promising framework for computing reliable policies in the face of model errors. Many successful reinforcement learning algorithms build on variations of policy-gradient methods, but adapting these methods to RMDPs has been challenging. As a result, the applicability of RMDPs to large, practical domains remains limited. This paper proposes a new Double-Loop Robust Policy Gradient (DRPG), the first generic policy gradient method for RMDPs. In contrast with prior robust policy gradient algorithms, DRPG monotonically reduces approximation errors to guarantee convergence to a globally optimal policy in tabular RMDPs. We introduce a novel parametric transition kernel and solve the inner loop robust policy via a gradient-based method. Finally, our numerical results demonstrate the utility of our new algorithm and confirm its global convergence properties.

Tremendous progress has been made in reinforcement learning (RL) over the past decade. Most of these advancements came through the continual development of new algorithms, which were designed using a combination of mathematical derivations, intuitions, and experimentation. Such an approach of creating algorithms manually is limited by human understanding and ingenuity. In contrast, meta-learning provides a toolkit for automatic machine learning method optimisation, potentially addressing this flaw. However, black-box approaches which attempt to discover RL algorithms with minimal prior structure have thus far not outperformed existing hand-crafted algorithms. Mirror Learning, which includes RL algorithms, such as PPO, offers a potential middle-ground starting point: while every method in this framework comes with theoretical guarantees, components that differentiate them are subject to design. In this paper we explore the Mirror Learning space by meta-learning a "drift" function. We refer to the immediate result as Learnt Policy Optimisation (LPO). By analysing LPO we gain original insights into policy optimisation which we use to formulate a novel, closed-form RL algorithm, Discovered Policy Optimisation (DPO). Our experiments in Brax environments confirm state-of-the-art performance of LPO and DPO, as well as their transfer to unseen settings.

Reinforcement Learning with Human Feedback (RLHF) has achieved great success in aligning large language models (LLMs) with human preferences. Prevalent RLHF approaches are reward-based, following the Bradley-Terry (BT) model assumption, which may not fully capture the complexity of human preferences. In this paper, we explore RLHF under a general preference framework and approach it from a game-theoretic perspective. Specifically, we formulate the problem as a two-player game and propose a novel algorithm, iterative Nash policy optimization (INPO). The key idea is to let the policy play against itself via no-regret learning, thereby approximating the Nash policy. Unlike previous methods, INPO bypasses the need for estimating the expected win rate for individual responses, which typically incurs high computational or annotation costs. Instead, we introduce a new loss objective that is directly minimized over a preference dataset. We provide theoretical analysis for our approach and demonstrate its effectiveness through experiments on various representative benchmarks. With an LLaMA-3-8B-based SFT model, INPO achieves a 41.5% length-controlled win rate on AlpacaEval 2.0 and a 38.3% win rate on Arena-Hard, showing substantial improvement over the state-of-the-art iterative algorithm [Dong et al., 2024] under the BT model assumption. Additionally, our ablation study highlights the benefits of incorporating KL regularization for response length control.

Group Relative Policy Optimization (GRPO) is a prominent reinforcement learning algorithm for post-training Large Language Models (LLMs). It is commonly believed that GRPO necessitates a large group size to ensure stable training via precise statistical estimation, which incurs substantial computational overhead. In this work, we challenge this assumption by reframing GRPO as a form of contrastive learning, which reveals a fundamental connection to Direct Preference Optimization (DPO). Motivated by DPO's empirical success, we investigate the minimal two-rollout case (2-GRPO), a configuration previously deemed infeasible. We provide a rigorous theoretical analysis to validate 2-GRPO and demonstrate empirically that it achieves performance on par with 16-GRPO, despite using only 1/8 of the rollouts and reducing training time by over 70%.

When fine-tuning pre-trained Large Language Models (LLMs) to align with human values and intentions, maximizing the estimated reward can lead to superior performance, but it also introduces potential risks due to deviations from the reference model's intended behavior. Most existing methods typically introduce KL divergence to constrain deviations between the trained model and the reference model; however, this may not be sufficient in certain applications that require tight risk control. In this paper, we introduce Risk-aware Direct Preference Optimization (Ra-DPO), a novel approach that incorporates risk-awareness by employing a class of nested risk measures. This approach formulates a constrained risk-aware advantage function maximization problem and then converts the Bradley-Terry model into a token-level representation. The objective function maximizes the likelihood of the policy while suppressing the deviation between a trained model and the reference model using a sequential risk ratio, thereby enhancing the model's risk-awareness. Experimental results across three open-source datasets: IMDb Dataset, Anthropic HH Dataset, and AlpacaEval, demonstrate the proposed method's superior performance in balancing alignment performance and model drift. Our code is opensourced at https://github.com/zlj123-max/Ra-DPO.

Direct Preference Optimization (DPO) has become a widely used training method for the instruction fine-tuning of large language models (LLMs). In this work, we explore an under-investigated aspect of DPO - its dependency on the reference model or policy. Such reference policies, typically instantiated as the model to be further fine-tuned, are important since they can impose an upper limit on DPO's effectiveness. Therefore, we address three related research questions in this work. First, we explore the optimal strength of the KL-divergence constraint in DPO, which penalizes deviations from the reference policy, and find that DPO is sensitive to this strength. Next, we examine the necessity of reference policies for instruction fine-tuning by providing both theoretical and empirical comparisons between DPO and related learning objectives, demonstrating DPO's superiority. Additionally, we investigate whether DPO benefits from stronger reference policies, finding that a stronger reference policy can lead to improved performance, but only when it is similar to the model being fine-tuned. Our findings highlight the confounding role of reference policies in DPO and offer insights for best practices, while also identifying open research questions for future studies.

The alignment of language models with human preferences is vital for their application in real-world tasks. The problem is formulated as optimizing the model's policy to maximize the expected reward that reflects human preferences with minimal deviation from the initial policy. While considered as a straightforward solution, reinforcement learning (RL) suffers from high variance in policy updates, which impedes efficient policy improvement. Recently, direct preference optimization (DPO) was proposed to directly optimize the policy from preference data. Though simple to implement, DPO is derived based on the optimal policy that is not assured to be achieved in practice, which undermines its convergence to the intended solution. In this paper, we propose efficient exact optimization (EXO) of the alignment objective. We prove that EXO is guaranteed to optimize in the same direction as the RL algorithms asymptotically for arbitary parametrization of the policy, while enables efficient optimization by circumventing the complexities associated with RL algorithms. We compare our method to DPO with both theoretical and empirical analyses, and further demonstrate the advantages of our method over existing approaches on realistic human preference data.

Closed-loop decision-making systems (e.g., lending, screening, or recidivism risk assessment) often operate under fairness and service constraints while inducing feedback effects: decisions change who appears in the future, yielding non-stationary data and potentially amplifying disparities. We study online learning of a one-dimensional threshold policy from bandit feedback under demographic parity (DP) and, optionally, service-rate constraints. The learner observes only a scalar score each round and selects a threshold; reward and constraint residuals are revealed only for the chosen threshold. We propose Optimistic Feasible Search (OFS), a simple grid-based method that maintains confidence bounds for reward and constraint residuals for each candidate threshold. At each round, OFS selects a threshold that appears feasible under confidence bounds and, among those, maximizes optimistic reward; if no threshold appears feasible, OFS selects the threshold minimizing optimistic constraint violation. This design directly targets feasible high-utility thresholds and is particularly effective for low-dimensional, interpretable policy classes where discretization is natural. We evaluate OFS on (i) a synthetic closed-loop benchmark with stable contraction dynamics and (ii) two semi-synthetic closed-loop benchmarks grounded in German Credit and COMPAS, constructed by training a score model and feeding group-dependent acceptance decisions back into population composition. Across all environments, OFS achieves higher reward with smaller cumulative constraint violation than unconstrained and primal-dual bandit baselines, and is near-oracle relative to the best feasible fixed threshold under the same sweep procedure. Experiments are reproducible and organized with double-blind-friendly relative outputs.

The wide popularity of short videos on social media poses new opportunities and challenges to optimize recommender systems on the video-sharing platforms. Users sequentially interact with the system and provide complex and multi-faceted responses, including watch time and various types of interactions with multiple videos. One the one hand, the platforms aims at optimizing the users' cumulative watch time (main goal) in long term, which can be effectively optimized by Reinforcement Learning. On the other hand, the platforms also needs to satisfy the constraint of accommodating the responses of multiple user interactions (auxiliary goals) such like, follow, share etc. In this paper, we formulate the problem of short video recommendation as a Constrained Markov Decision Process (CMDP). We find that traditional constrained reinforcement learning algorithms can not work well in this setting. We propose a novel two-stage constrained actor-critic method: At stage one, we learn individual policies to optimize each auxiliary signal. At stage two, we learn a policy to (i) optimize the main signal and (ii) stay close to policies learned at the first stage, which effectively guarantees the performance of this main policy on the auxiliaries. Through extensive offline evaluations, we demonstrate effectiveness of our method over alternatives in both optimizing the main goal as well as balancing the others. We further show the advantage of our method in live experiments of short video recommendations, where it significantly outperforms other baselines in terms of both watch time and interactions. Our approach has been fully launched in the production system to optimize user experiences on the platform.

Direct Preference Optimization (DPO) and its variants have become standard for aligning Large Language Models due to their simplicity and offline stability. However, we identify two fundamental limitations. First, the optimal policy depends on arbitrary modeling choices (scalarization function, reference policy), yielding behavior reflecting parameterization artifacts rather than true preferences. Second, treating response generation in isolation fails to leverage comparative information in pairwise data, leaving the model's capacity for intrinsic self-reflection untapped. To address it, we propose Intrinsic Self-reflective Preference Optimization (InSPO), deriving a globally optimal policy conditioning on both context and alternative responses. We prove this formulation superior to DPO/RLHF while guaranteeing invariance to scalarization and reference choices. InSPO serves as a plug-and-play enhancement without architectural changes or inference overhead. Experiments demonstrate consistent improvements in win rates and length-controlled metrics, validating that unlocking self-reflection yields more robust, human-aligned LLMs. Our Code is available at https://github.com/Skylanding/InSPO.

We introduce Feasible Learning (FL), a sample-centric learning paradigm where models are trained by solving a feasibility problem that bounds the loss for each training sample. In contrast to the ubiquitous Empirical Risk Minimization (ERM) framework, which optimizes for average performance, FL demands satisfactory performance on every individual data point. Since any model that meets the prescribed performance threshold is a valid FL solution, the choice of optimization algorithm and its dynamics play a crucial role in shaping the properties of the resulting solutions. In particular, we study a primal-dual approach which dynamically re-weights the importance of each sample during training. To address the challenge of setting a meaningful threshold in practice, we introduce a relaxation of FL that incorporates slack variables of minimal norm. Our empirical analysis, spanning image classification, age regression, and preference optimization in large language models, demonstrates that models trained via FL can learn from data while displaying improved tail behavior compared to ERM, with only a marginal impact on average performance.

On-policy reinforcement learning (RL), particularly Proximal Policy Optimization (PPO) and Group Relative Policy Optimization (GRPO), has become the dominant paradigm for fine-tuning large language models (LLMs). While policy ratio clipping stabilizes training, this heuristic hard constraint incurs a fundamental cost: it indiscriminately truncates gradients from high-return yet high-divergence actions, suppressing rare but highly informative "eureka moments" in complex reasoning. Moreover, once data becomes slightly stale, hard clipping renders it unusable, leading to severe sample inefficiency. In this work, we revisit the trust-region objective in policy optimization and show that explicitly constraining the variance (second central moment) of the policy ratio provides a principled and smooth relaxation of hard clipping. This distributional constraint stabilizes policy updates while preserving gradient signals from valuable trajectories. Building on this insight, we propose R^2VPO (Ratio-Variance Regularized Policy Optimization), a novel primal-dual framework that supports stable on-policy learning and enables principled off-policy data reuse by dynamically reweighting stale samples rather than discarding them. We extensively evaluate R^2VPO on fine-tuning state-of-the-art LLMs, including DeepSeek-Distill-Qwen-1.5B and the openPangu-Embedded series (1B and 7B), across challenging mathematical reasoning benchmarks. Experimental results show that R^2VPO consistently achieves superior asymptotic performance, with average relative gains of up to 17% over strong clipping-based baselines, while requiring approximately 50% fewer rollouts to reach convergence. These findings establish ratio-variance control as a promising direction for improving both stability and data efficiency in RL-based LLM alignment.

Direct alignment algorithms such as Direct Preference Optimization (DPO) fine-tune models based on preference data, using only supervised learning instead of two-stage reinforcement learning with human feedback (RLHF). We show that DPO encodes a statistical estimation problem over reward functions induced by a parametric policy class. When the true reward function that generates preferences cannot be realized via the policy class, DPO becomes misspecified, resulting in failure modes such as preference order reversal, worsening of policy reward, and high sensitivity to the input preference data distribution. On the other hand, we study the local behavior of two-stage RLHF for a parametric class and relate it to a natural gradient step in policy space. Our fine-grained geometric characterization allows us to propose AuxDPO, which introduces additional auxiliary variables in the DPO loss function to help move towards the RLHF solution in a principled manner and mitigate the misspecification in DPO. We empirically demonstrate the superior performance of AuxDPO on didactic bandit settings as well as LLM alignment tasks.

Continual learning aims to enable a single model to learn a sequence of tasks without catastrophic forgetting. Top-performing methods usually require a rehearsal buffer to store past pristine examples for experience replay, which, however, limits their practical value due to privacy and memory constraints. In this work, we present a simple yet effective framework, DualPrompt, which learns a tiny set of parameters, called prompts, to properly instruct a pre-trained model to learn tasks arriving sequentially without buffering past examples. DualPrompt presents a novel approach to attach complementary prompts to the pre-trained backbone, and then formulates the objective as learning task-invariant and task-specific "instructions". With extensive experimental validation, DualPrompt consistently sets state-of-the-art performance under the challenging class-incremental setting. In particular, DualPrompt outperforms recent advanced continual learning methods with relatively large buffer sizes. We also introduce a more challenging benchmark, Split ImageNet-R, to help generalize rehearsal-free continual learning research. Source code is available at https://github.com/google-research/l2p.

Decision-making under distribution shift is a central challenge in reinforcement learning (RL), where training and deployment environments differ. We study this problem through the lens of robust Markov decision processes (RMDPs), which optimize performance against adversarial transition dynamics. Our focus is the online setting, where the agent has only limited interaction with the environment, making sample efficiency and exploration especially critical. Policy optimization, despite its success in standard RL, remains theoretically and empirically underexplored in robust RL. To bridge this gap, we propose Distributionally Robust Regularized Policy Optimization algorithm (DR-RPO), a model-free online policy optimization method that learns robust policies with sublinear regret. To enable tractable optimization within the softmax policy class, DR-RPO incorporates reference-policy regularization, yielding RMDP variants that are doubly constrained in both transitions and policies. To scale to large state-action spaces, we adopt the d-rectangular linear MDP formulation and combine linear function approximation with an upper confidence bonus for optimistic exploration. We provide theoretical guarantees showing that policy optimization can achieve polynomial suboptimality bounds and sample efficiency in robust RL, matching the performance of value-based approaches. Finally, empirical results across diverse domains corroborate our theory and demonstrate the robustness of DR-RPO.

As LLMs advance, post-training reinforcement learning (RL) increasingly relies on multi-dimensional rewards to cultivate comprehensive capabilities. This shift demands new algorithms capable of optimizing diverse and potentially competing objectives simultaneously. To address this, existing methods such as Group reward-Decoupled Policy Optimization (GDPO) decompose the overall score into independent reward groups, then compute the RL loss separately within each group. However, this strategy still encounters multi-reward conflicts: a single rollout can yield positive advantages on certain reward dimensions but negative ones on others, causing opposing signals to cancel each other out during aggregation, further hindering RL training efficiency. Inspired by Dynamic sAmpling Policy Optimization (DAPO), which improves RL training efficiency by filtering out ineffective rollouts with near-zero advantages, we propose Group-Dynamic reward-Decoupled Policy Optimization (GD^2PO). Specifically, GD^2PO employs a conflict-aware filtering mechanism to mask out rollouts suffering from severe reward-wise disagreement. By preventing conflicting signals from canceling each other out, this masking strategy preserves and enhances the magnitude of effective RL advantages, thereby significantly accelerating learning efficiency. Furthermore, we introduce query-level reweighting to dynamically adjust the update intensity of each query based on its overall reward consensus. Experiments on various multi-reward scenarios, including tool calling and human preference alignment, demonstrate that GD^2PO consistently and significantly outperforms existing baselines. The code is available at https://github.com/Qwen-Applications/GD2PO.

We introduce Diffusion Policy Policy Optimization, DPPO, an algorithmic framework including best practices for fine-tuning diffusion-based policies (e.g. Diffusion Policy) in continuous control and robot learning tasks using the policy gradient (PG) method from reinforcement learning (RL). PG methods are ubiquitous in training RL policies with other policy parameterizations; nevertheless, they had been conjectured to be less efficient for diffusion-based policies. Surprisingly, we show that DPPO achieves the strongest overall performance and efficiency for fine-tuning in common benchmarks compared to other RL methods for diffusion-based policies and also compared to PG fine-tuning of other policy parameterizations. Through experimental investigation, we find that DPPO takes advantage of unique synergies between RL fine-tuning and the diffusion parameterization, leading to structured and on-manifold exploration, stable training, and strong policy robustness. We further demonstrate the strengths of DPPO in a range of realistic settings, including simulated robotic tasks with pixel observations, and via zero-shot deployment of simulation-trained policies on robot hardware in a long-horizon, multi-stage manipulation task. Website with code: diffusion-ppo.github.io

Reinforcement learning (RL) has recently become the core paradigm for aligning and strengthening large language models (LLMs). Yet, applying RL in off-policy settings--where stale data from past policies are used for training--improves sample efficiency, but remains challenging: policy entropy declines sharply, optimization often becomes unstable and may even collapse. Through theoretical and empirical analysis, we identify two key insights: (i) an imbalance in optimization, where negative-advantage samples dominate the policy gradient, suppressing useful behaviors and risking gradient explosions; and (ii) the derived Entropy-Clip Rule, which reveals that the fixed clipping mechanism in PPO-like objectives systematically blocks entropy-increasing updates, thereby driving the policy toward over-exploitation at the expense of exploration. Building on these insights, we propose BAlanced Policy Optimization with Adaptive Clipping (BAPO), a simple yet effective method that dynamically adjusts clipping bounds to adaptively re-balance positive and negative contributions, preserve entropy, and stabilize RL optimization. Across diverse off-policy scenarios--including sample replay and partial rollout--BAPO achieves fast, stable, and data-efficient training. On AIME 2024 and AIME 2025 benchmarks, our 7B BAPO model surpasses open-source counterparts such as SkyWork-OR1-7B, while our 32B BAPO model not only achieves state-of-the-art results among models of the same scale but also outperforms leading proprietary systems like o3-mini and Gemini-2.5-Flash-Thinking.

Model-free reinforcement learning algorithms have seen remarkable progress, but key challenges remain. Trust Region Policy Optimization (TRPO) is known for ensuring monotonic policy improvement through conservative updates within a trust region, backed by strong theoretical guarantees. However, its reliance on complex second-order optimization limits its practical efficiency. Proximal Policy Optimization (PPO) addresses this by simplifying TRPO's approach using ratio clipping, improving efficiency but sacrificing some theoretical robustness. This raises a natural question: Can we combine the strengths of both methods? In this paper, we introduce Simple Policy Optimization (SPO), a novel unconstrained first-order algorithm. By slightly modifying the policy loss used in PPO, SPO can achieve the best of both worlds. Our new objective improves upon ratio clipping, offering stronger theoretical properties and better constraining the probability ratio within the trust region. Empirical results demonstrate that SPO outperforms PPO with a simple implementation, particularly for training large, complex network architectures end-to-end.

Recent advances in large language models (LLMs) have greatly improved their reasoning and decision-making abilities when deployed as agents. Richer reasoning, however, often comes at the cost of longer chain of thought (CoT), hampering interaction efficiency in real-world scenarios. Nevertheless, there still lacks systematic definition of LLM agent efficiency, hindering targeted improvements. To this end, we introduce dual-efficiency, comprising (i) step-level efficiency, which minimizes tokens per step, and (ii) trajectory-level efficiency, which minimizes the number of steps to complete a task. Building on this definition, we propose DEPO, a dual-efficiency preference optimization method that jointly rewards succinct responses and fewer action steps. Experiments on WebShop and BabyAI show that DEPO cuts token usage by up to 60.9% and steps by up to 26.9%, while achieving up to a 29.3% improvement in performance. DEPO also generalizes to three out-of-___domain math benchmarks and retains its efficiency gains when trained on only 25% of the data. Our project page is at https://opencausalab.github.io/DEPO.

In proactive dialogue, the challenge lies not just in generating responses but in steering conversations toward predetermined goals, a task where Large Language Models (LLMs) typically struggle due to their reactive nature. Traditional approaches to enhance dialogue planning in LLMs, ranging from elaborate prompt engineering to the integration of policy networks, either face efficiency issues or deliver suboptimal performance. Inspired by the dualprocess theory in psychology, which identifies two distinct modes of thinking - intuitive (fast) and analytical (slow), we propose the Dual-Process Dialogue Planning (DPDP) framework. DPDP embodies this theory through two complementary planning systems: an instinctive policy model for familiar contexts and a deliberative Monte Carlo Tree Search (MCTS) mechanism for complex, novel scenarios. This dual strategy is further coupled with a novel two-stage training regimen: offline Reinforcement Learning for robust initial policy model formation followed by MCTS-enhanced on-the-fly learning, which ensures a dynamic balance between efficiency and strategic depth. Our empirical evaluations across diverse dialogue tasks affirm DPDP's superiority in achieving both high-quality dialogues and operational efficiency, outpacing existing methods.

Reinforcement Learning (RL) from Human Preference-based feedback is a popular paradigm for fine-tuning generative models, which has produced impressive models such as GPT-4 and Claude3 Opus. This framework often consists of two steps: learning a reward model from an offline preference dataset followed by running online RL to optimize the learned reward model. In this work, leveraging the idea of reset, we propose a new RLHF algorithm with provable guarantees. Motivated by the fact that offline preference dataset provides informative states (i.e., data that is preferred by the labelers), our new algorithm, Dataset Reset Policy Optimization (DR-PO), integrates the existing offline preference dataset into the online policy training procedure via dataset reset: it directly resets the policy optimizer to the states in the offline dataset, instead of always starting from the initial state distribution. In theory, we show that DR-PO learns to perform at least as good as any policy that is covered by the offline dataset under general function approximation with finite sample complexity. In experiments, we demonstrate that on both the TL;DR summarization and the Anthropic Helpful Harmful (HH) dataset, the generation from DR-PO is better than that from Proximal Policy Optimization (PPO) and Direction Preference Optimization (DPO), under the metric of GPT4 win-rate. Code for this work can be found at https://github.com/Cornell-RL/drpo.

Offline-to-online reinforcement learning (RL) is a training paradigm that combines pre-training on a pre-collected dataset with fine-tuning in an online environment. However, the incorporation of online fine-tuning can intensify the well-known distributional shift problem. Existing solutions tackle this problem by imposing a policy constraint on the policy improvement objective in both offline and online learning. They typically advocate a single balance between policy improvement and constraints across diverse data collections. This one-size-fits-all manner may not optimally leverage each collected sample due to the significant variation in data quality across different states. To this end, we introduce Family Offline-to-Online RL (FamO2O), a simple yet effective framework that empowers existing algorithms to determine state-adaptive improvement-constraint balances. FamO2O utilizes a universal model to train a family of policies with different improvement/constraint intensities, and a balance model to select a suitable policy for each state. Theoretically, we prove that state-adaptive balances are necessary for achieving a higher policy performance upper bound. Empirically, extensive experiments show that FamO2O offers a statistically significant improvement over various existing methods, achieving state-of-the-art performance on the D4RL benchmark. Codes are available at https://github.com/LeapLabTHU/FamO2O.

The effectiveness of Direct Preference Optimization (DPO) depends on preference data that reflect the quality differences that matter in multimodal tasks. Existing pipelines often rely on off-policy perturbations or coarse outcome-based signals, which are not well suited to fine-grained visual reasoning. We propose rDPO, a preference optimization framework based on instance-specific rubrics. For each image-instruction pair, we create a checklist-style rubric of essential and additional criteria to score responses from any possible policies. The instruction-rubric pool is built offline and reused during the construction of on-policy data. On public reward modeling benchmarks, rubric-based prompting massively improves a 30B-A3B judge and brings it close to GPT-5.4. On public downstream benchmarks, rubric-based filtering raises the macro average to 82.69, whereas outcome-based filtering drops it to 75.82 from 81.14. When evaluating scalability on a comprehensive benchmark, rDPO achieves 61.01, markedly outperforming the style-constrained baseline (52.36) and surpassing the 59.48 base model. Together, these results show that visual preference optimization benefits from combining on-policy data construction with instance-specific criterion-level feedback.

Reinforcement Learning (RL) post-training has become the standard for aligning generative models with human preferences, yet most methods rely on a single scalar reward. When multiple criteria matter, the prevailing practice of ``early scalarization'' collapses rewards into a fixed weighted sum. This commits the model to a single trade-off point at training time, providing no inference-time control over inherently conflicting goals -- such as prompt adherence versus source fidelity in image editing. We introduce ParetoSlider, a multi-objective RL (MORL) framework that trains a single diffusion model to approximate the entire Pareto front. By training the model with continuously varying preference weights as a conditioning signal, we enable users to navigate optimal trade-offs at inference time without retraining or maintaining multiple checkpoints. We evaluate ParetoSlider across three state-of-the-art flow-matching backbones: SD3.5, FluxKontext, and LTX-2. Our single preference-conditioned model matches or exceeds the performance of baselines trained separately for fixed reward trade-offs, while uniquely providing fine-grained control over competing generative goals.

On-policy reinforcement learning methods like GRPO suffer from mode collapse: they exhibit reduced solution diversity, concentrating probability mass on a single solution once discovered and ceasing exploration of alternative strategies. We show this stems from reverse KL minimization's mode-seeking behavior, which reinforces the first high-reward trajectory found rather than maintaining a distribution over multiple diverse solutions. We propose DMPO (Distribution-Matching Policy Optimization), which prevents mode collapse through principled approximation of forward KL minimization. DMPO constructs a group level target distribution over sampled trajectories proportional to their rewards, then aligns the policy distribution to this target. This provides mode-covering behavior without requiring sampling from the intractable global target distribution, enabling sustained exploration throughout training. We validate DMPO on NP-hard combinatorial optimization, where exponentially many feasible solutions exist but only a few approach optimality, an ideal testbed for evaluating exploration. DMPO achieves 43.9% Quality Ratio on text-based NP-Bench (vs. GRPO's 40.1%) and 43.1% on vision-based NP-Bench (vs. 38.4%), demonstrating 9% and 12% relative improvements respectively. These gains generalize to mathematical reasoning (+2.0%) and out-of-___domain tasks (+2.3%), showing that diversity-preserving training enhances general reasoning capabilities across modalities. Our work establishes distribution matching as a practical, principled approach to preventing mode collapse in on-policy RL, with consistent quality improvements demonstrating sustained exploration across diverse reasoning tasks.

As language models become increasingly capable, users expect them to provide not only accurate responses but also behaviors aligned with diverse human preferences across a variety of scenarios. To achieve this, Reinforcement learning (RL) pipelines have begun incorporating multiple rewards, each capturing a distinct preference, to guide models toward these desired behaviors. However, recent work has defaulted to apply Group Relative Policy Optimization (GRPO) under multi-reward setting without examining its suitability. In this paper, we demonstrate that directly applying GRPO to normalize distinct rollout reward combinations causes them to collapse into identical advantage values, reducing the resolution of the training signal and resulting in suboptimal convergence and, in some cases, early training failure. We then introduce Group reward-Decoupled Normalization Policy Optimization (GDPO), a new policy optimization method to resolve these issues by decoupling the normalization of individual rewards, more faithfully preserving their relative differences and enabling more accurate multi-reward optimization, along with substantially improved training stability. We compare GDPO with GRPO across three tasks: tool calling, math reasoning, and coding reasoning, evaluating both correctness metrics (accuracy, bug ratio) and constraint adherence metrics (format, length). Across all settings, GDPO consistently outperforms GRPO, demonstrating its effectiveness and generalizability for multi-reward reinforcement learning optimization.

We revisit Group Relative Policy Optimization (GRPO) in both on-policy and off-policy optimization regimes. Our motivation comes from recent work on off-policy Proximal Policy Optimization (PPO), which improves training stability, sampling efficiency, and memory usage. In addition, a recent analysis of GRPO suggests that estimating the advantage function with off-policy samples could be beneficial. Building on these observations, we adapt GRPO to the off-policy setting. We show that both on-policy and off-policy GRPO objectives yield an improvement in the reward. This result motivates the use of clipped surrogate objectives in the off-policy version of GRPO. We then compare the empirical performance of reinforcement learning with verifiable rewards in post-training using both GRPO variants. Our results show that off-policy GRPO either significantly outperforms or performs on par with its on-policy counterpart.

In the field of large language models (LLMs), aligning models with the diverse preferences of users is a critical challenge. Direct Preference Optimization (DPO) has played a key role in this area. It works by using pairs of preferences derived from the same prompts, and it functions without needing an additional reward model. However, DPO does not fully reflect the complex nature of human learning, which often involves understanding contrasting responses to not only identical but also similar questions. To overcome this shortfall, we propose Relative Preference Optimization (RPO). RPO is designed to discern between more and less preferred responses derived from both identical and related prompts. It introduces a contrastive weighting mechanism, enabling the tuning of LLMs using a broader range of preference data, including both paired and unpaired sets. This approach expands the learning capabilities of the model, allowing it to leverage insights from a more varied set of prompts. Through empirical tests, including dialogue and summarization tasks, and evaluations using the AlpacaEval2.0 leaderboard, RPO has demonstrated a superior ability to align LLMs with user preferences and to improve their adaptability during the training process. Our code can be viewed at https://github.com/yinyueqin/relative-preference-optimization

Markov Decision Processes (MDPs) are a formal framework for modeling and solving sequential decision-making problems. In finite-time horizons such problems are relevant for instance for optimal stopping or specific supply chain problems, but also in the training of large language models. In contrast to infinite horizon MDPs optimal policies are not stationary, policies must be learned for every single epoch. In practice all parameters are often trained simultaneously, ignoring the inherent structure suggested by dynamic programming. This paper introduces a combination of dynamic programming and policy gradient called dynamic policy gradient, where the parameters are trained backwards in time. For the tabular softmax parametrisation we carry out the convergence analysis for simultaneous and dynamic policy gradient towards global optima, both in the exact and sampled gradient settings without regularisation. It turns out that the use of dynamic policy gradient training much better exploits the structure of finite-time problems which is reflected in improved convergence bounds.

The exploration-exploitation (EE) trade-off is a central challenge in reinforcement learning (RL) for large language models (LLMs). With Group Relative Policy Optimization (GRPO), training tends to be exploitation driven: entropy decreases monotonically, samples convergence, and exploration fades. Most existing fixes are sample-centric: they seek or bonus rare samples, assuming exploration comes from novel trajectories and tokens. These heuristics depend on the "luck" of informative samples, lack principled control of the policy, and often yield limited or inconsistent gains. In this work, we are the first to introduce a distribution-centric perspective for RL, in which exploration is always guided by a "better" target distribution, and reveal that a policy's ability to resist entropy collapse is governed by the distribution itself rather than individual samples. Building on this insight, we propose Distribution-Centric Policy Optimization (DCPO), which reformulates entropy regulation as distribution-level regularization. DCPO achieves controllable entropy fully on-policy without sampling from external distributions, enabling efficient exploration while maintaining training stability. Across multiple models and seven benchmarks, DCPO improves over GRPO by about 20\% on average. Overall, DCPO replaces sample-level heuristics with distribution-level principles, offering a theoretically grounded and flexible framework for controllable exploration and a stronger EE trade-off. The code is available in https://github.com/597358816/DCPO.

Direct preference optimization (DPO) is a form of reinforcement learning from human feedback (RLHF) where the policy is learned directly from preferential feedback. Although many models of human preferences exist, the critical task of selecting the most informative feedback for training them is under-explored. We propose an active learning framework for DPO, which can be applied to collect human feedback online or to choose the most informative subset of already collected feedback offline. We propose efficient algorithms for both settings. The key idea is to linearize the DPO objective at the last layer of the neural network representation of the optimized policy and then compute the D-optimal design to collect preferential feedback. We prove that the errors in our DPO logit estimates diminish with more feedback. We show the effectiveness of our algorithms empirically in the setting that matches our theory and also on large language models.

Multi-objective reinforcement learning (MORL) approaches have emerged to tackle many real-world problems with multiple conflicting objectives by maximizing a joint objective function weighted by a preference vector. These approaches find fixed customized policies corresponding to preference vectors specified during training. However, the design constraints and objectives typically change dynamically in real-life scenarios. Furthermore, storing a policy for each potential preference is not scalable. Hence, obtaining a set of Pareto front solutions for the entire preference space in a given ___domain with a single training is critical. To this end, we propose a novel MORL algorithm that trains a single universal network to cover the entire preference space scalable to continuous robotic tasks. The proposed approach, Preference-Driven MORL (PD-MORL), utilizes the preferences as guidance to update the network parameters. It also employs a novel parallelization approach to increase sample efficiency. We show that PD-MORL achieves up to 25% larger hypervolume for challenging continuous control tasks and uses an order of magnitude fewer trainable parameters compared to prior approaches.

In the post-training of large language models (LLMs), Reinforcement Learning from Human Feedback (RLHF) is an effective approach to achieve generation aligned with human preferences. Direct Preference Optimization (DPO) allows for policy training with a simple binary cross-entropy loss without a reward model. The objective of DPO is regularized by reverse KL divergence that encourages mode-seeking fitting to the reference policy. Nonetheless, we indicate that minimizing reverse KL divergence could fail to capture a mode of the reference distribution, which may hurt the policy's performance. Based on this observation, we propose a simple modification to DPO, H-DPO, which allows for control over the entropy of the resulting policy, enhancing the distribution's sharpness and thereby enabling mode-seeking fitting more effectively. In our experiments, we show that H-DPO outperformed DPO across various tasks, demonstrating superior results in pass@k evaluations for mathematical tasks. Moreover, H-DPO is simple to implement, requiring only minor modifications to the loss calculation of DPO, which makes it highly practical and promising for wide-ranging applications in the training of LLMs.

Polypharmacy, most often defined as the simultaneous consumption of five or more drugs at once, is a prevalent phenomenon in the older population. Some of these polypharmacies, deemed inappropriate, may be associated with adverse health outcomes such as death or hospitalization. Considering the combinatorial nature of the problem as well as the size of claims database and the cost to compute an exact association measure for a given drug combination, it is impossible to investigate every possible combination of drugs. Therefore, we propose to optimize the search for potentially inappropriate polypharmacies (PIPs). To this end, we propose the OptimNeuralTS strategy, based on Neural Thompson Sampling and differential evolution, to efficiently mine claims datasets and build a predictive model of the association between drug combinations and health outcomes. We benchmark our method using two datasets generated by an internally developed simulator of polypharmacy data containing 500 drugs and 100 000 distinct combinations. Empirically, our method can detect up to 72% of PIPs while maintaining an average precision score of 99% using 30 000 time steps.

The prevalent deployment of learning from human preferences through reinforcement learning (RLHF) relies on two important approximations: the first assumes that pairwise preferences can be substituted with pointwise rewards. The second assumes that a reward model trained on these pointwise rewards can generalize from collected data to out-of-distribution data sampled by the policy. Recently, Direct Preference Optimisation (DPO) has been proposed as an approach that bypasses the second approximation and learn directly a policy from collected data without the reward modelling stage. However, this method still heavily relies on the first approximation. In this paper we try to gain a deeper theoretical understanding of these practical algorithms. In particular we derive a new general objective called PsiPO for learning from human preferences that is expressed in terms of pairwise preferences and therefore bypasses both approximations. This new general objective allows us to perform an in-depth analysis of the behavior of RLHF and DPO (as special cases of PsiPO) and to identify their potential pitfalls. We then consider another special case for PsiPO by setting Psi simply to Identity, for which we can derive an efficient optimisation procedure, prove performance guarantees and demonstrate its empirical superiority to DPO on some illustrative examples.

Reinforcement learning from human feedback (RLHF) has been extensively employed to align large language models with user intent. However, proximal policy optimization (PPO) based RLHF is occasionally unstable requiring significant hyperparameter finetuning, and computationally expensive to maximize the estimated reward during alignment. Recently, direct preference optimization (DPO) is proposed to address those challenges. However, DPO relies on contrastive responses generated from human annotator and alternative LLM, instead of the policy model, limiting the effectiveness of the RLHF. In this paper, we addresses both challenges by systematically combining rejection sampling (RS) and DPO. Our proposed method, RS-DPO, initiates with the development of a supervised fine-tuned policy model (SFT). A varied set of k responses per prompt are sampled directly from the SFT model. RS-DPO identifies pairs of contrastive samples based on their reward distribution. Finally, we apply DPO with the contrastive samples to align the model to human preference. Our experiments indicate that our proposed method effectively fine-tunes LLMs with limited resource environments, leading to improved alignment with user intent. Furthermore, it outperforms existing methods, including RS, PPO, and DPO.

Reinforcement Learning from Human Feedback (RLHF) has emerged as a pivotal tool for aligning large language models (LLMs) with human preferences. Direct Preference Optimization (DPO), one of the most popular approaches, formulates RLHF as a policy optimization problem without explicitly estimating the reward function. It overcomes the stability and efficiency issues of two-step approaches, which typically involve first estimating the reward function and then optimizing the policy via proximal policy optimization (PPO). Since RLHF is essentially an optimization problem, and it is well-known that momentum techniques can accelerate optimization both theoretically and empirically, a natural question arises: Can RLHF be accelerated by momentum? This paper answers this question in the affirmative. In detail, we first show that the iterative preference optimization method can be viewed as a proximal point method. Based on this observation, we propose a general Accelerated Preference Optimization (APO) framework, which unifies many existing preference optimization algorithms and employs Nesterov's momentum technique to speed up the alignment of LLMs. Theoretically, we demonstrate that APO can achieve a faster convergence rate than the standard iterative preference optimization methods, including DPO and Self-Play Preference Optimization (SPPO). Empirically, we show the superiority of APO over DPO, iterative DPO, and other strong baselines for RLHF on the AlpacaEval 2.0 benchmark.

Because it is difficult to precisely specify complex objectives, reinforcement learning policies are often optimized using proxy reward functions that only approximate the true goal. However, optimizing proxy rewards frequently leads to reward hacking: the optimized reward function ceases to be a good proxy and the resulting policy performs poorly with respect to the unspecified true reward. Principled solutions to reward hacking have been impeded by the lack of a good definition for the problem. To address this gap, we introduce a definition of reward hacking based on the correlation between proxy and true rewards for states and actions seen by a "base policy" that breaks down under optimization. We show that this definition captures reward hacking behavior across several realistic settings, including in reinforcement learning from human feedback (RLHF). Using our formulation, we show theoretically that regularization to the base policy can effectively prevent reward hacking. While the current practice in RLHF applies a KL penalty between action distributions for this purpose, our theory suggests regularizing the chi^2 divergence between the policies' occupancy measures can be more effective. We intuitively show the benefits of this type of regularization and demonstrate that it better mitigates reward hacking in practice across four realistic settings, including RLHF. Our code is available at https://github.com/cassidylaidlaw/orpo.

Aligning language models with human preferences relies on pairwise preference datasets. While some studies suggest that on-policy data consistently outperforms off -policy data for preference learning, others indicate that the advantages of on-policy data may be task-dependent, highlighting the need for a systematic exploration of their interplay. In this work, we show that on-policy and off-policy data offer complementary strengths in preference optimization: on-policy data is particularly effective for reasoning tasks like math and coding, while off-policy data performs better on open-ended tasks such as creative writing and making personal recommendations. Guided by these findings, we introduce SIMPLEMIX, an approach to combine the complementary strengths of on-policy and off-policy preference learning by simply mixing these two data sources. Our empirical results across diverse tasks and benchmarks demonstrate that SIMPLEMIX substantially improves language model alignment. Specifically, SIMPLEMIX improves upon on-policy DPO and off-policy DPO by an average of 6.03% on Alpaca Eval 2.0. Moreover, it outperforms prior approaches that are much more complex in combining on- and off-policy data, such as HyPO and DPO-Mix-P, by an average of 3.05%.

Direct Preference Optimization (DPO) has become a popular approach for aligning language models using pairwise preferences. However, in practical post-training pipelines, on-policy generation typically yields multiple candidate responses per prompt, which are scored by a reward model to guide learning. In this setting, we propose Multi-Preference Optimization (MPO), a generalization of DPO that optimizes over entire sets of responses by extending the Bradley-Terry model to groupwise comparisons between chosen and rejected sets. To further enhance learning, MPO employs deviation-based weighting, which emphasizes outlier responses that deviate most from the mean reward, effectively inducing a self-paced curriculum. We theoretically prove that MPO reduces alignment bias at a rate of Oleft(1{n}right) with respect to the number of responses per query. Empirically, MPO achieves state-of-the-art performance on the UltraFeedback benchmark and yields up to sim 17.5% improvement over the state-of-the-art baseline in length-controlled win rate on AlpacaEval2, establishing a new baseline for preference-based alignment

Incorporating safety is an essential prerequisite for broadening the practical applications of reinforcement learning in real-world scenarios. To tackle this challenge, Constrained Markov Decision Processes (CMDPs) are leveraged, which introduce a distinct cost function representing safety violations. In CMDPs' settings, Lagrangian relaxation technique has been employed in previous algorithms to convert constrained optimization problems into unconstrained dual problems. However, these algorithms may inaccurately predict unsafe behavior, resulting in instability while learning the Lagrange multiplier. This study introduces a novel safe reinforcement learning algorithm, Safety Critic Policy Optimization (SCPO). In this study, we define the safety critic, a mechanism that nullifies rewards obtained through violating safety constraints. Furthermore, our theoretical analysis indicates that the proposed algorithm can automatically balance the trade-off between adhering to safety constraints and maximizing rewards. The effectiveness of the SCPO algorithm is empirically validated by benchmarking it against strong baselines.

Off-policy reinforcement learning (RL) has proven to be a powerful framework for guiding agents' actions in environments with stochastic rewards and unknown or noisy state dynamics. In many real-world settings, these agents must operate in multiple environments, each with slightly different dynamics. For example, we may be interested in developing policies to guide medical treatment for patients with and without a given disease, or policies to navigate curriculum design for students with and without a learning disability. Here, we introduce nested policy fitted Q-iteration (NFQI), an RL framework that finds optimal policies in environments that exhibit such a structure. Our approach develops a nested Q-value function that takes advantage of the shared structure between two groups of observations from two separate environments while allowing their policies to be distinct from one another. We find that NFQI yields policies that rely on relevant features and perform at least as well as a policy that does not consider group structure. We demonstrate NFQI's performance using an OpenAI Gym environment and a clinical decision making RL task. Our results suggest that NFQI can develop policies that are better suited to many real-world clinical environments.

Online advertising has recently grown into a highly competitive and complex multi-billion-dollar industry, with advertisers bidding for ad slots at large scales and high frequencies. This has resulted in a growing need for efficient "auto-bidding" algorithms that determine the bids for incoming queries to maximize advertisers' targets subject to their specified constraints. This work explores efficient online algorithms for a single value-maximizing advertiser under an increasingly popular constraint: Return-on-Spend (RoS). We quantify efficiency in terms of regret relative to the optimal algorithm, which knows all queries a priori. We contribute a simple online algorithm that achieves near-optimal regret in expectation while always respecting the specified RoS constraint when the input sequence of queries are i.i.d. samples from some distribution. We also integrate our results with the previous work of Balseiro, Lu, and Mirrokni [BLM20] to achieve near-optimal regret while respecting both RoS and fixed budget constraints. Our algorithm follows the primal-dual framework and uses online mirror descent (OMD) for the dual updates. However, we need to use a non-canonical setup of OMD, and therefore the classic low-regret guarantee of OMD, which is for the adversarial setting in online learning, no longer holds. Nonetheless, in our case and more generally where low-regret dynamics are applied in algorithm design, the gradients encountered by OMD can be far from adversarial but influenced by our algorithmic choices. We exploit this key insight to show our OMD setup achieves low regret in the realm of our algorithm.

Multi-step learning applies lookahead over multiple time steps and has proved valuable in policy evaluation settings. However, in the optimal control case, the impact of multi-step learning has been relatively limited despite a number of prior efforts. Fundamentally, this might be because multi-step policy improvements require operations that cannot be approximated by stochastic samples, hence hindering the widespread adoption of such methods in practice. To address such limitations, we introduce doubly multi-step off-policy VI (DoMo-VI), a novel oracle algorithm that combines multi-step policy improvements and policy evaluations. DoMo-VI enjoys guaranteed convergence speed-up to the optimal policy and is applicable in general off-policy learning settings. We then propose doubly multi-step off-policy actor-critic (DoMo-AC), a practical instantiation of the DoMo-VI algorithm. DoMo-AC introduces a bias-variance trade-off that ensures improved policy gradient estimates. When combined with the IMPALA architecture, DoMo-AC has showed improvements over the baseline algorithm on Atari-57 game benchmarks.

We describe an iterative procedure for optimizing policies, with guaranteed monotonic improvement. By making several approximations to the theoretically-justified procedure, we develop a practical algorithm, called Trust Region Policy Optimization (TRPO). This algorithm is similar to natural policy gradient methods and is effective for optimizing large nonlinear policies such as neural networks. Our experiments demonstrate its robust performance on a wide variety of tasks: learning simulated robotic swimming, hopping, and walking gaits; and playing Atari games using images of the screen as input. Despite its approximations that deviate from the theory, TRPO tends to give monotonic improvement, with little tuning of hyperparameters.

Counterfactual Risk Minimization (CRM) is a framework for dealing with the logged bandit feedback problem, where the goal is to improve a logging policy using offline data. In this paper, we explore the case where it is possible to deploy learned policies multiple times and acquire new data. We extend the CRM principle and its theory to this scenario, which we call "Sequential Counterfactual Risk Minimization (SCRM)." We introduce a novel counterfactual estimator and identify conditions that can improve the performance of CRM in terms of excess risk and regret rates, by using an analysis similar to restart strategies in accelerated optimization methods. We also provide an empirical evaluation of our method in both discrete and continuous action settings, and demonstrate the benefits of multiple deployments of CRM.

Mirror descent (MD), a well-known first-order method in constrained convex optimization, has recently been shown as an important tool to analyze trust-region algorithms in reinforcement learning (RL). However, there remains a considerable gap between such theoretically analyzed algorithms and the ones used in practice. Inspired by this, we propose an efficient RL algorithm, called {\em mirror descent policy optimization} (MDPO). MDPO iteratively updates the policy by {\em approximately} solving a trust-region problem, whose objective function consists of two terms: a linearization of the standard RL objective and a proximity term that restricts two consecutive policies to be close to each other. Each update performs this approximation by taking multiple gradient steps on this objective function. We derive {\em on-policy} and {\em off-policy} variants of MDPO, while emphasizing important design choices motivated by the existing theory of MD in RL. We highlight the connections between on-policy MDPO and two popular trust-region RL algorithms: TRPO and PPO, and show that explicitly enforcing the trust-region constraint is in fact {\em not} a necessity for high performance gains in TRPO. We then show how the popular soft actor-critic (SAC) algorithm can be derived by slight modifications of off-policy MDPO. Overall, MDPO is derived from the MD principles, offers a unified approach to viewing a number of popular RL algorithms, and performs better than or on-par with TRPO, PPO, and SAC in a number of continuous control tasks. Code is available at https://github.com/manantomar/Mirror-Descent-Policy-Optimization.

Recently, advanced large language models (LLMs) have emerged at an increasingly rapid pace. However, when faced with complex problems, most users are often unable to provide accurate and effective prompts to interact with LLMs, thus limiting the performance of LLMs. To address this challenge, we propose Prompt-R1, an end-to-end reinforcement learning framework that uses a small-scale LLM to collaborate with large-scale LLMs, replacing user interaction to solve problems better. This collaboration is cast as a multi-turn prompt interaction, where the small-scale LLM thinks and generates prompts, and the large-scale LLM performs complex reasoning. A dual-constrained reward is designed to optimize for correctness, generation quality, and reasoning accuracy. Prompt-R1 provides a plug-and-play framework that supports both inference and training with various large-scale LLMs. Experiments on multiple public datasets show that Prompt-R1 significantly outperforms baseline models across tasks. Our code is publicly available at https://github.com/QwenQKing/Prompt-R1.

We present a fine-grained theoretical analysis of the performance gap between reinforcement learning from human feedback (RLHF) and direct preference optimization (DPO) under a representation gap. Our study decomposes this gap into two sources: an explicit representation gap under exact optimization and an implicit representation gap under finite samples. In the exact optimization setting, we characterize how the relative capacities of the reward and policy model classes influence the final policy qualities. We show that RLHF, DPO, or online DPO can outperform one another depending on the type of model mis-specifications. Notably, online DPO can outperform both RLHF and standard DPO when the reward and policy model classes are isomorphic and both mis-specified. In the approximate optimization setting, we provide a concrete construction where the ground-truth reward is implicitly sparse and show that RLHF requires significantly fewer samples than DPO to recover an effective reward model -- highlighting a statistical advantage of two-stage learning. Together, these results provide a comprehensive understanding of the performance gap between RLHF and DPO under various settings, and offer practical insights into when each method is preferred.

The phenomenon of model-wise double descent, where the test error peaks and then reduces as the model size increases, is an interesting topic that has attracted the attention of researchers due to the striking observed gap between theory and practice Belkin2018ReconcilingMM. Additionally, while double descent has been observed in various tasks and architectures, the peak of double descent can sometimes be noticeably absent or diminished, even without explicit regularization, such as weight decay and early stopping. In this paper, we investigate this intriguing phenomenon from the optimization perspective and propose a simple optimization-based explanation for why double descent sometimes occurs weakly or not at all. To the best of our knowledge, we are the first to demonstrate that many disparate factors contributing to model-wise double descent (initialization, normalization, batch size, learning rate, optimization algorithm) are unified from the viewpoint of optimization: model-wise double descent is observed if and only if the optimizer can find a sufficiently low-loss minimum. These factors directly affect the condition number of the optimization problem or the optimizer and thus affect the final minimum found by the optimizer, reducing or increasing the height of the double descent peak. We conduct a series of controlled experiments on random feature models and two-layer neural networks under various optimization settings, demonstrating this optimization-based unified view. Our results suggest the following implication: Double descent is unlikely to be a problem for real-world machine learning setups. Additionally, our results help explain the gap between weak double descent peaks in practice and strong peaks observable in carefully designed setups.

Standard reinforcement learning from human feedback (RLHF) trains a reward model on pairwise preference data and then uses it for policy optimization. However, while reward models are optimized to capture relative preferences, existing policy optimization techniques rely on absolute reward magnitudes during training. In settings where the rewards are non-verifiable such as summarization, instruction following, and chat completion, this misalignment often leads to suboptimal performance. We introduce Group Ordinal Policy Optimization (GOPO), a policy optimization method that uses only the ranking of the rewards and discards their magnitudes. Our rank-based transformation of rewards provides several gains, compared to Group Relative Policy Optimization (GRPO), in settings with non-verifiable rewards: (1) consistently higher training/validation reward trajectories, (2) improved LLM-as-judge evaluations across most intermediate training steps, and (3) reaching a policy of comparable quality in substantially less training steps than GRPO. We demonstrate consistent improvements across a range of tasks and model sizes.

Trust Region Policy Optimization (TRPO) is a popular and empirically successful policy search algorithm in reinforcement learning (RL). It iteratively solved the surrogate problem which restricts consecutive policies to be close to each other. TRPO is an on-policy algorithm. On-policy methods bring many benefits, like the ability to gauge each resulting policy. However, they typically discard all the knowledge about the policies which existed before. In this work, we use a replay buffer to borrow from the off-policy learning setting to TRPO. Entropy regularization is usually used to improve policy optimization in reinforcement learning. It is thought to aid exploration and generalization by encouraging more random policy choices. We add an Entropy regularization term to advantage over π, accumulated over time steps, in TRPO. We call this update EnTRPO. Our experiments demonstrate EnTRPO achieves better performance for controlling a Cart-Pole system compared with the original TRPO

Many sequential decision-making tasks involve optimizing multiple conflicting objectives, requiring policies that adapt to different user preferences. In multi-objective reinforcement learning (MORL), one widely studied approach} addresses this by training a single policy network conditioned on preference-weighted rewards. In this paper, we explore a novel algorithmic perspective: leveraging reward-free reinforcement learning (RFRL) for MORL. While RFRL has historically been studied independently of MORL, it learns optimal policies for any possible reward function, making it a natural fit for MORL's challenge of handling unknown user preferences. We propose using the RFRL's training objective as an auxiliary task to enhance MORL, enabling more effective knowledge sharing beyond the multi-objective reward function given at training time. To this end, we adapt a state-of-the-art RFRL algorithm to the MORL setting and introduce a preference-guided exploration strategy that focuses learning on relevant parts of the environment. Through extensive experiments and ablation studies, we demonstrate that our approach significantly outperforms the state-of-the-art MORL methods across diverse MO-Gymnasium tasks, achieving superior performance and data efficiency. This work provides the first systematic adaptation of RFRL to MORL, demonstrating its potential as a scalable and empirically effective solution to multi-objective policy learning.

Budget management strategies in repeated auctions have received growing attention in online advertising markets. However, previous work on budget management in online bidding mainly focused on second-price auctions. The rapid shift from second-price auctions to first-price auctions for online ads in recent years has motivated the challenging question of how to bid in repeated first-price auctions while controlling budgets. In this work, we study the problem of learning in repeated first-price auctions with budgets. We design a dual-based algorithm that can achieve a near-optimal O(T) regret with full information feedback where the maximum competing bid is always revealed after each auction. We further consider the setting with one-sided information feedback where only the winning bid is revealed after each auction. We show that our modified algorithm can still achieve an O(T) regret with mild assumptions on the bidder's value distribution. Finally, we complement the theoretical results with numerical experiments to confirm the effectiveness of our budget management policy.

Reinforcement Learning with Verifiable Rewards (RLVR) has emerged as a promising paradigm for post-training reasoning models. However, group-based methods such as Group Relative Policy Optimization (GRPO) face a critical dilemma in sparse-reward settings: pure Reinforcement Learning (RL) suffers from advantage collapse and high-variance gradient estimation, while mixed-policy optimization introduces persistent distributional bias. To resolve this dilemma, we introduce Hindsight-Anchored Policy Optimization (HAPO). HAPO employs the Synthetic Success Injection (SSI) operator, a hindsight mechanism that selectively anchors optimization to teacher demonstrations during failure. This injection is governed by a Thompson sampling-inspired gating mechanism, creating an autonomous, self-paced curriculum. Theoretically, we demonstrate that HAPO achieves asymptotic consistency: by naturally annealing the teacher signal as the policy improves, HAPO recovers the unbiased on-policy gradient. This ensures off-policy guidance acts as a temporary scaffold rather than a persistent ceiling, enabling the model to surpass the limitations of static teacher forcing.

Critique-guided reinforcement learning (RL) has emerged as a powerful paradigm for training LLM agents by augmenting sparse outcome rewards with natural-language feedback. However, current methods often rely on static or offline critic models, which fail to adapt as the policy evolves. In on-policy RL, the agent's error patterns shift over time, causing stationary critics to become stale and providing feedback of diminishing utility. To address this, we introduce ECHO (Evolving Critic for Hindsight-Guided Optimization)}, a framework that jointly optimizes the policy and critic through a synchronized co-evolutionary loop. ECHO utilizes a cascaded rollout mechanism where the critic generates multiple diagnoses for an initial trajectory, followed by policy refinement to enable group-structured advantage estimation. We address the challenge of learning plateaus via a saturation-aware gain shaping objective, which rewards the critic for inducing incremental improvements in high-performing trajectories. By employing dual-track GRPO updates, ECHO ensures the critic's feedback stays synchronized with the evolving policy. Experimental results show that ECHO yields more stable training and higher long-horizon task success across open-world environments.

We argue that inventory management presents unique opportunities for the reliable application of deep reinforcement learning (DRL). To enable this, we emphasize and test two complementary techniques. The first is Hindsight Differentiable Policy Optimization (HDPO), which uses pathwise gradients from offline counterfactual simulations to directly and efficiently optimize policy performance. Unlike standard policy gradient methods that rely on high-variance score-function estimators, HDPO computes gradients by differentiating through the known system dynamics. Via extensive benchmarking, we show that HDPO recovers near-optimal policies in settings with known or bounded optima, is more robust than variants of the REINFORCE algorithm, and significantly outperforms generalized newsvendor heuristics on problems using real time series data. Our second technique aligns neural policy architectures with the topology of the inventory network. We exploit Graph Neural Networks (GNNs) as a natural inductive bias for encoding supply chain structure, demonstrate that they can represent optimal and near-optimal policies in two theoretical settings, and empirically show that they reduce data requirements across six diverse inventory problems. A key obstacle to progress in this area is the lack of standardized benchmark problems. To address this gap, we open-source a suite of benchmark environments, along with our full codebase, to promote transparency and reproducibility. All resources are available at github.com/MatiasAlvo/Neural_inventory_control.

Policy optimization methods are popular reinforcement learning algorithms in practice. Recent works have built theoretical foundation for them by proving T regret bounds even when the losses are adversarial. Such bounds are tight in the worst case but often overly pessimistic. In this work, we show that in tabular Markov decision processes (MDPs), by properly designing the regularizer, the exploration bonus and the learning rates, one can achieve a more favorable polylog(T) regret when the losses are stochastic, without sacrificing the worst-case guarantee in the adversarial regime. To our knowledge, this is also the first time a gap-dependent polylog(T) regret bound is shown for policy optimization. Specifically, we achieve this by leveraging a Tsallis entropy or a Shannon entropy regularizer in the policy update. Then we show that under known transitions, we can further obtain a first-order regret bound in the adversarial regime by leveraging the log-barrier regularizer.

Offline reinforcement learning (RL) optimizes the policy on a previously collected dataset without any interactions with the environment, yet usually suffers from the distributional shift problem. To mitigate this issue, a typical solution is to impose a policy constraint on a policy improvement objective. However, existing methods generally adopt a ``one-size-fits-all'' practice, i.e., keeping only a single improvement-constraint balance for all the samples in a mini-batch or even the entire offline dataset. In this work, we argue that different samples should be treated with different policy constraint intensities. Based on this idea, a novel plug-in approach named Guided Offline RL (GORL) is proposed. GORL employs a guiding network, along with only a few expert demonstrations, to adaptively determine the relative importance of the policy improvement and policy constraint for every sample. We theoretically prove that the guidance provided by our method is rational and near-optimal. Extensive experiments on various environments suggest that GORL can be easily installed on most offline RL algorithms with statistically significant performance improvements.

We study the problem of learning minimax policies in zero-sum matrix games. Fiegel et al. (2025) recently showed that achieving last-iterate convergence in this setting is harder when the players are uncoupled, by proving a lower bound on the exploitability gap of Omega(t^{-1/4}). Some online mirror descent algorithms were proposed in the literature for this problem, but none have truly attained this rate yet. We show that the use of a log-barrier regularization, along with a dual-focused analysis, allows this O-tilde(t^{-1/4}) convergence with high-probability. We additionally extend our idea to the setting of extensive-form games, proving a bound with the same rate.

Preference optimization methods typically begin training with a well-trained SFT model as a reference model. In RLHF and DPO, a regularization term is used during the preference optimization process to prevent the policy model from deviating too far from the reference model's distribution, thereby avoiding the generation of anomalous responses. When the reference model is already well-aligned with the given data or only requires slight adjustments, this approach can produce a well-aligned model. However, if the reference model is not aligned with the given data and requires significant deviation from its current state, a regularization term may actually hinder the model alignment. In this study, we propose Modulated Intervention Preference Optimization (MIPO) to address this issue. MIPO modulates the degree of intervention from the reference model based on how well the given data is aligned with it. If the data is well-aligned, the intervention is increased to prevent the policy model from diverging significantly from reference model. Conversely, if the alignment is poor, the interference is reduced to facilitate more extensive training. We compare the performance of MIPO and DPO using Mistral-7B and Llama3-8B in Alpaca Eval 2.0 and MT-Bench. The experimental results demonstrate that MIPO consistently outperforms DPO across various evaluation scenarios.

Reinforcement learning is a framework for learning to act sequentially in an unknown environment. We propose a natural approach for modeling policy structure in policy gradients. The key idea is to optimize for a subset of future rewards: smaller subsets represent simpler policies, which can be learned more reliably because their empirical gradient estimates are more accurate. Our approach allows for modeling and comparison of different policy classes, including full planning, greedy, K-step lookahead, and segment policies. We evaluate the policies empirically on multiple persona-alignment conversational problems. Different policies excel in different problems, reflecting their different characteristics and highlighting the importance of our studied policy class.

We study the optimisation problem associated with Gaussian process regression using squared loss. The most common approach to this problem is to apply an exact solver, such as conjugate gradient descent, either directly, or to a reduced-order version of the problem. Recently, driven by successes in deep learning, stochastic gradient descent has gained traction as an alternative. In this paper, we show that when done rightx2014by which we mean using specific insights from the optimisation and kernel communitiesx2014this approach is highly effective. We thus introduce a particular stochastic dual gradient descent algorithm, that may be implemented with a few lines of code using any deep learning framework. We explain our design decisions by illustrating their advantage against alternatives with ablation studies and show that the new method is highly competitive. Our evaluations on standard regression benchmarks and a Bayesian optimisation task set our approach apart from preconditioned conjugate gradients, variational Gaussian process approximations, and a previous version of stochastic gradient descent for Gaussian processes. On a molecular binding affinity prediction task, our method places Gaussian process regression on par in terms of performance with state-of-the-art graph neural networks.

Reinforcement learning from human feedback (RLHF) is one of the key techniques that helps large language models (LLMs) to follow instructions and provide helpful and harmless responses. While direct policy optimization methods exist, state-of-the-art LLMs adopt RL-based methods (usually PPO) in RLHF to train the policy to generate good responses guided by a reward model learned from preference data. The main challenge of these methods is the inaccuracy of the intermediate reward model, especially in code generation tasks that require long and complex reasoning to score a response. We find that the reliability of the reward model varies across responses assigned with different rewards. This motivates us to filter the samples whose rewards may be unreliable to improve signal-to-noise ratio during policy learning, resulting in Policy Filtration for Proximal Policy Optimization (PF-PPO). To choose a proper policy filtration strategy for a given reward model, the coefficient of determination (R^2) between rewards and actual scores on filtered samples serves as a good metrics and helps us find several promising strategies. We provide extensive experiments to validate the effectiveness of PF-PPO in code generation tasks, and find that some variants of PF-PPO are highly effective and achieve new state-of-the-art performance across 7-billion-parameter models on HumanEval, MBPP, and a new and more challenging LeetCode Contest benchmark.

Large Language Models (LLMs) have shown promising capabilities for solving Operations Research (OR) problems. While reinforcement learning serves as a powerful paradigm for LLM training on OR problems, existing works generally face two key limitations. First, outcome reward suffers from the credit assignment problem, where correct final answers can reinforce flawed reasoning. Second, conventional discriminative process supervision is myopic, failing to evaluate the interdependent steps of OR modeling holistically. To this end, we introduce StepORLM, a novel self-evolving framework with generative process supervision. At its core, StepORLM features a co-evolutionary loop where a policy model and a generative process reward model (GenPRM) iteratively improve on each other. This loop is driven by a dual-feedback mechanism: definitive, outcome-based verification from an external solver, and nuanced, holistic process evaluation from the GenPRM. The combined signal is used to align the policy via Weighted Direct Preference Optimization (W-DPO) and simultaneously refine the GenPRM. Our resulting 8B-parameter StepORLM establishes a new state-of-the-art across six benchmarks, significantly outperforming vastly larger generalist models, agentic methods, and specialized baselines. Moreover, the co-evolved GenPRM is able to act as a powerful and universally applicable process verifier, substantially boosting the inference scaling performance of both our own model and other existing LLMs.

Reinforcement learning from human feedback (RLHF) is a standard approach for fine-tuning large language models to follow instructions. As part of this process, learned reward models are used to approximately model human preferences. However, as imperfect representations of the "true" reward, these learned reward models are susceptible to overoptimization. Gao et al. (2023) studied this phenomenon in a synthetic human feedback setup with a significantly larger "gold" reward model acting as the true reward (instead of humans) and showed that overoptimization remains a persistent problem regardless of the size of the proxy reward model and training data used. Using a similar setup, we conduct a systematic study to evaluate the efficacy of using ensemble-based conservative optimization objectives, specifically worst-case optimization (WCO) and uncertainty-weighted optimization (UWO), for mitigating reward model overoptimization when using two optimization methods: (a) best-of-n sampling (BoN) (b) proximal policy optimization (PPO). We additionally extend the setup of Gao et al. (2023) to include 25% label noise to better mirror real-world conditions. Both with and without label noise, we find that conservative optimization practically eliminates overoptimization and improves performance by up to 70% for BoN sampling. For PPO, ensemble-based conservative optimization always reduces overoptimization and outperforms single reward model optimization. Moreover, combining it with a small KL penalty successfully prevents overoptimization at no performance cost. Overall, our results demonstrate that ensemble-based conservative optimization can effectively counter overoptimization.

While online Reinforcement Learning has emerged as a crucial technique for aligning flow matching models with human preferences, current approaches are hindered by inefficient exploration during training rollouts. Relying on undirected stochasticity and sparse outcome rewards, these methods struggle to discover high-reward samples, resulting in data-inefficient and slow optimization. To address these limitations, we propose Euphonium, a novel framework that steers generation via process reward gradient guided dynamics. Our key insight is to formulate the sampling process as a theoretically principled Stochastic Differential Equation that explicitly incorporates the gradient of a Process Reward Model into the flow drift. This design enables dense, step-by-step steering toward high-reward regions, advancing beyond the unguided exploration in prior works, and theoretically encompasses existing sampling methods (e.g., Flow-GRPO, DanceGRPO) as special cases. We further derive a distillation objective that internalizes the guidance signal into the flow network, eliminating inference-time dependency on the reward model. We instantiate this framework with a Dual-Reward Group Relative Policy Optimization algorithm, combining latent process rewards for efficient credit assignment with pixel-level outcome rewards for final visual fidelity. Experiments on text-to-video generation show that Euphonium achieves better alignment compared to existing methods while accelerating training convergence by 1.66x.

In problem-solving, we humans can come up with multiple novel solutions to the same problem. However, reinforcement learning algorithms can only produce a set of monotonous policies that maximize the cumulative reward but lack diversity and novelty. In this work, we address the problem of generating novel policies in reinforcement learning tasks. Instead of following the multi-objective framework used in existing methods, we propose to rethink the problem under a novel perspective of constrained optimization. We first introduce a new metric to evaluate the difference between policies and then design two practical novel policy generation methods following the new perspective. The two proposed methods, namely the Constrained Task Novel Bisector (CTNB) and the Interior Policy Differentiation (IPD), are derived from the feasible direction method and the interior point method commonly known in the constrained optimization literature. Experimental comparisons on the MuJoCo control suite show our methods can achieve substantial improvement over previous novelty-seeking methods in terms of both the novelty of policies and their performances in the primal task.

Direct Preference Optimization (DPO) has emerged as a cornerstone of reinforcement learning from human feedback (RLHF) due to its simplicity and efficiency. However, existing DPO-based methods typically treat all preference pairs equally, overlooking substantial variations in data quality and learning difficulty, which leads to inefficient data utilization and suboptimal performance. To address this limitation, we propose Uni-DPO, a unified dynamic preference optimization framework that jointly considers (a) the inherent quality of preference pairs and (b) the model's evolving performance during training. By adaptively reweighting samples based on both factors, Uni-DPO enables more effective use of preference data and achieves superior performance. Extensive experiments across models and benchmarks demonstrate the effectiveness and generalization of Uni-DPO. On textual tasks, Gemma-2-9B-IT fine-tuned with Uni-DPO surpasses the leading LLM, Claude 3 Opus, by 6.7 points on Arena-Hard. On mathematical and multimodal tasks, Uni-DPO consistently outperforms baseline methods across all benchmarks, providing strong empirical evidence of its effectiveness and robustness.

Sequential decision-making problems with multiple objectives arise naturally in practice and pose unique challenges for research in decision-theoretic planning and learning, which has largely focused on single-objective settings. This article surveys algorithms designed for sequential decision-making problems with multiple objectives. Though there is a growing body of literature on this subject, little of it makes explicit under what circumstances special methods are needed to solve multi-objective problems. Therefore, we identify three distinct scenarios in which converting such a problem to a single-objective one is impossible, infeasible, or undesirable. Furthermore, we propose a taxonomy that classifies multi-objective methods according to the applicable scenario, the nature of the scalarization function (which projects multi-objective values to scalar ones), and the type of policies considered. We show how these factors determine the nature of an optimal solution, which can be a single policy, a convex hull, or a Pareto front. Using this taxonomy, we survey the literature on multi-objective methods for planning and learning. Finally, we discuss key applications of such methods and outline opportunities for future work.

Recent mixed-policy optimization methods for LLM reasoning that interleave or blend supervised and reinforcement learning signals report improvements over the standard SFT-then-RL pipeline. We show that numerous recently published research papers rely on a faulty baseline caused by two distinct bugs: a CPU-offloaded optimizer bug in DeepSpeed that silently drops intermediate micro-batches during gradient accumulation (affecting multiple downstream frameworks including TRL, OpenRLHF and Llama-Factory), and a loss aggregation bug in OpenRLHF that incorrectly weights per-mini-batch losses. Together they suppress SFT performance, with the optimizer bug accounting for most of the gap and the loss aggregation bug contributing a smaller additional effect. Once corrected, the standard SFT-then-RL pipeline surpasses every published mixed-policy method we evaluate by +3.8 points on math benchmarks with Qwen2.5-Math-7B and by +22.2 points with Llama-3.1-8B. Even a truncated variant with just 50 RL steps outperforms mixed-policy methods on math benchmarks while using fewer FLOPs.

We propose a new family of policy gradient methods for reinforcement learning, which alternate between sampling data through interaction with the environment, and optimizing a "surrogate" objective function using stochastic gradient ascent. Whereas standard policy gradient methods perform one gradient update per data sample, we propose a novel objective function that enables multiple epochs of minibatch updates. The new methods, which we call proximal policy optimization (PPO), have some of the benefits of trust region policy optimization (TRPO), but they are much simpler to implement, more general, and have better sample complexity (empirically). Our experiments test PPO on a collection of benchmark tasks, including simulated robotic locomotion and Atari game playing, and we show that PPO outperforms other online policy gradient methods, and overall strikes a favorable balance between sample complexity, simplicity, and wall-time.

Optimization (PPO) has been positioned by recent literature as the canonical method for the RL part of RLHF. PPO performs well empirically but has a heuristic motivation and handles the KL-divergence constraint used in LM-RLHF in an ad-hoc manner and suffers form reward oscillations, entropy collapse, value function drift, and sudden policy divergence that require frequent restarts and extensive hyperparameter tuning. In this paper, we develop a new pure on policy actor-critic RL method for the LM-RLHF setting. We present SAFE (Stable Alignment Finetuning with Entropy-aware control),a novel RLHF algorithm that combines a Double Soft-Min Critic for pessimistic value estimation with a new multi-layer stabilization framework combining entropy-gated KL regulation, and PID-controlled adaptive thresholds. Unlike standard PPO's symmetric KL penalties, SAFE distinguishes high-entropy exploration from low-entropy mode collapse and adjusts penalties dynamically based on reward velocity. Experiments on a 3B parameter model show SAFE achieves +5.15\% training-average reward than PPO (0.725 vs 0.689), negligible reward crashes, and superior KL control than ppo . Our method adds minimal computational overhead and provides an interpretable, crash-resistant RLHF framework that maintains aggressive learning speed while ensuring stable long-horizon optimization suitable for production deployment. Code is available at https://github.com/ryyzn9/SAFE