This article considers the decentralized composite optimization problem. We propose a novel decentralized variance-reduction proximal-gradient algorithmic framework, called PMGT-VR, which combines several techniques, including multi-consensus, gradient tracking, and variance reduction. The proposed framework imitates centralized algorithms and algorithms under this framework achieve convergence rates similar to that of their centralized counterparts. We also describe and analyze two representative algorithms, PMGT-SAGA and PMGT-LSVRG, and compare them to existing state-of-the-art proximal algorithms. To the best of our knowledge, PMGT-VR is the first linearly convergent decentralized stochastic algorithm that can solve decentralized composite optimization problems. Numerical experiments are provided to demonstrate the effectiveness of the proposed algorithms.

In this paper, we study format biases in reinforcement learning from human feedback (RLHF).We observe that many widely-used preference models-including human evaluators, GPT-4, and top-ranking models on the RewardBench benchmark-exhibit strong biases towards specific format patterns, such as lists, links, bold text, and emojis.Furthermore, large language models (LLMs) can exploit these biases to achieve higher rankings on popular benchmarks like AlpacaEval and LMSYS Chatbot Arena.One notable example is verbosity bias, where current preference models favor longer responses that appear more comprehensive, even when their quality is equal to or lower than shorter responses.However, format biases beyond verbosity remain largely underexplored.In this work, we extend the study of biases in preference learning beyond the commonly recognized length bias, offering a comprehensive analysis of a wider range of format biases.Additionally, we show that with a small amount of biased data (less than 1%), we can inject significant bias into the reward model.Moreover, these format biases can also be easily exploited by downstream alignment algorithms, such as best-of-n sampling and online iterative DPO, as it is usually easier to manipulate the format than to improve the quality of responses.Our findings emphasize the need to disentangle format and content both for designing alignment algorithms and evaluating models.

Reward models (RMs) play a pivotal role in aligning large language models (LLMs) with human preferences. However, traditional RM training, which relies on response pairs tied to specific prompts, struggles to disentangle prompt-driven preferences from prompt-independent artifacts, such as response length and format. In this work, we expose a fundamental limitation of current RM training methods, where RMs fail to effectively distinguish between contextual signals and irrelevant artifacts when determining preferences. To address this, we introduce a causal framework that learns preferences independent of these artifacts and propose a novel data augmentation technique designed to eliminate them. Extensive experiments show that our approach successfully filters out undesirable artifacts, yielding a more robust reward model (RRM). Our RRM improves the performance of a pairwise reward model trained on Gemma-2-9b-it, on Reward-Bench, increasing accuracy from 80.61% to 84.15%. Additionally, we train two DPO policies using both the RM and RRM, demonstrating that the RRM significantly enhances DPO-aligned policies, improving MT-Bench scores from 7.27 to 8.31 and length-controlled win-rates in AlpacaEval-2 from 33.46% to 52.49%.

Recent studies have shown that large language models' (LLMs) mathematical problem-solving capabilities can be enhanced by integrating external tools, such as code interpreters, and employing multi-turn Chain-of-Thought (CoT) reasoning. While current methods focus on synthetic data generation and Supervised Fine-Tuning (SFT), this paper studies the complementary direct preference learning approach to further improve model performance. However, existing direct preference learning algorithms are originally designed for the single-turn chat task, and do not fully address the complexities of multi-turn reasoning and external tool integration required for tool-integrated mathematical reasoning tasks. To fill in this gap, we introduce a multi-turn direct preference learning framework, tailored for this context, that leverages feedback from code interpreters and optimizes trajectory-level preferences. This framework includes multi-turn DPO and multi-turn KTO as specific implementations. The effectiveness of our framework is validated through training of various language models using an augmented prompt set from the GSM8K and MATH datasets. Our results demonstrate substantial improvements: a supervised fine-tuned Gemma-1.1-it-7B model's performance increased from 77.5% to 83.9% on GSM8K and from 46.1% to 51.2% on MATH. Similarly, a Gemma-2-it-9B model improved from 84.1% to 86.3% on GSM8K and from 51.0% to 54.5% on MATH.

In the classical Reinforcement Learning from Human Feedback (RLHF) framework, Proximal Policy Optimization (PPO) is employed to learn from sparse, sentence-level rewards—a challenging scenario in traditional deep reinforcement learning. Despite the great successes of PPO in the alignment of state-of-the-art closed-source large language models (LLMs), its open-source implementation is still largely sub-optimal, as widely reported by numerous research studies. To address these issues, we introduce a framework that models RLHF problems as a Markov decision process (MDP), enabling the capture of fine-grained token-wise information. Furthermore, we provide theoretical insights that demonstrate the superiority of our MDP framework over the previous sentence-level bandit formulation. Under this framework, we introduce an algorithm, dubbed as Reinforced Token Optimization (RTO), which learns the token-wise reward function from preference data and performs policy optimization based on this learned token-wise reward signal. Theoretically, RTO is proven to have the capability of finding the near-optimal policy sample-efficiently. For its practical implementation, RTO innovatively integrates Direct Preference Optimization (DPO) and PPO. DPO, originally derived from sparse sentence rewards, surprisingly provides us with a token-wise characterization of response quality, which is seamlessly incorporated into our subsequent PPO training stage. We conduct extensive experiments to evaluate RTO against PPO and other direct preference learning algorithms. The results highlight the effectiveness of RTO, with the algorithm outperforming PPO by 7.5 points on the AlpacaEval 2 benchmark and by 4.1 points on Arena-Hard. Our code and models are available at https://github.com/zkshan2002/RTO.

Large Language Models (LLMs) have revolutionized artificial intelligence with capabilities in reasoning, coding, and communication, driving innovation across industries. Their true potential depends on effective alignment to ensure correct, trustworthy and ethical behavior, addressing challenges like misinformation, hallucinations, bias and misuse. While existing Reinforcement Learning (RL)-based alignment methods are notoriously complex, direct optimization approaches offer a simpler alternative. In this work, we introduce a novel direct optimization approach for LLM alignment by drawing on established Information Retrieval (IR) principles. We present a systematic framework that bridges LLM alignment and IR methodologies, mapping LLM generation and reward models to IR’s retriever-reranker paradigm. Building on this foundation, we propose LLM Alignment as Retriever Preference Optimization (LarPO), a new alignment method that enhances overall alignment quality. Extensive experiments validate LarPO’s effectiveness with 38.9 % and 13.7 % averaged improvement on AlpacaEval2 and MixEval-Hard respectively. Our work opens new avenues for advancing LLM alignment by integrating IR foundations, offering a promising direction for future research.

Recent advances in Reinforcement Learning from Human Feedback (RLHF) have shown that KL-regularization plays a pivotal role in improving the efficiency of RL fine-tuning for large language models (LLMs). Despite its empirical advantage, the theoretical difference between KL-regularized RL and standard RL remains largely under-explored. While there is a recent line of work on the theoretical analysis of KL-regularized objective in decision making (Xiong et al., 2024a; Xie et al., 2024; Zhao et al., 2024), these analyses either reduce to the traditional RL setting or rely on strong coverage assumptions. In this paper, we propose an optimism-based KL-regularized online contextual bandit algorithm, and provide a novel analysis of its regret. By carefully leveraging the benign optimization landscape induced by the KL-regularization and the optimistic reward estimation, our algorithm achieves an $\mathcal{O}\big(\eta\log (N_{\mathcal R} T)\cdot d_{\mathcal R}\big)$ logarithmic regret bound, where $\eta, N_{\mathcal R},T,d_{\mathcal R}$ denote the KL-regularization parameter, the cardinality of the reward function class, number of rounds, and the complexity of the reward function class. Furthermore, we extend our algorithm and analysis to reinforcement learning by developing a novel decomposition over transition steps and also obtain a similar logarithmic regret bound.

Chain-of-thought (CoT) reasoning in large language models (LLMs) can be formalized as a latent variable problem, where the model needs to generate intermediate reasoning steps. While prior approaches such as iterative reward-ranked fine-tuning (RAFT) have relied on such formulations, they typically apply uniform inference budgets across prompts, which fails to account for variability in difficulty and convergence behavior. This work identifies the main bottleneck in CoT training as inefficient stochastic gradient estimation due to static sampling strategies. We propose GVM-RAFT, a prompt-specific Dynamic Sample Allocation Strategy designed to minimize stochastic gradient variance under a computational budget constraint. The method dynamically allocates computational resources by monitoring prompt acceptance rates and stochastic gradient norms, ensuring that the resulting gradient variance is minimized. Our theoretical analysis shows that the proposed dynamic sampling strategy leads to accelerated convergence guarantees under suitable conditions. Experiments on mathematical reasoning show that GVM-RAFT achieves a 2-4x speedup and considerable accuracy improvements over vanilla RAFT. The proposed dynamic sampling strategy is general and can be incorporated into other reinforcement learning algorithms, such as GRPO, leading to similar improvements in convergence and test accuracy.

Haoxiang Wang, Yong Lin, Wei Xiong, Rui Yang, Shizhe Diao, Shuang Qiu, Han Zhao, Tong Zhang. Proceedings of the 62nd Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers). 2024.

Yong Lin, Hangyu Lin, Wei Xiong, Shizhe Diao, Jianmeng Liu, Jipeng Zhang, Rui Pan, Haoxiang Wang, Wenbin Hu, Hanning Zhang, Hanze Dong, Renjie Pi, Han Zhao, Nan Jiang, Heng Ji, Yuan Yao, Tong Zhang. Proceedings of the 2024 Conference on Empirical Methods in Natural Language Processing. 2024.

This paper studies the theoretical framework of the alignment process of generative models with Reinforcement Learning from Human Feedback (RLHF). We consider a standard mathematical formulation, the reverse-KL regularized contextual bandit for RLHF. Despite its widespread practical application, a rigorous theoretical analysis of this formulation remains open. We investigate its behavior in three distinct settings—offline, online, and hybrid—and propose efficient algorithms with finite-sample theoretical guarantees. Moving towards practical applications, our framework, with a robust approximation of the information-theoretical policy improvement oracle, naturally gives rise to several novel RLHF algorithms. This includes an iterative version of the Direct Preference Optimization (DPO) algorithm for online settings, and a multi-step rejection sampling strategy for offline scenarios. Our empirical evaluations on real-world alignment experiment of large language model demonstrate that these proposed methods significantly surpass existing strong baselines, such as DPO and Rejection Sampling Optimization (RSO), showcasing the connections between solid theoretical foundations and their potent practical implementations.

We investigate Reinforcement Learning from Human Feedback (RLHF) in the context of a general preference oracle. In particular, we do not assume the existence of a reward function and an oracle preference signal drawn from the Bradley-Terry model as most of the prior works do. We consider a standard mathematical formulation, the reverse-KL regularized minimax game between two LLMs for RLHF under general preference oracle. The learning objective of this formulation is to find a policy so that it is consistently preferred by the KL-regularized preference oracle over any competing LLMs. We show that this framework is strictly more general than the reward-based one, and propose sample-efficient algorithms for both the offline learning from a pre-collected preference dataset and online learning where we can query the preference oracle along the way of training. Empirical studies verify the effectiveness of the proposed framework.

Existing theoretical studies on offline reinforcement learning (RL) mostly consider a dataset sampled directly from the target task. In practice, however, data often come from several heterogeneous but related sources. Motivated by this gap, this work aims at rigorously understanding offline RL with multiple datasets that are collected from randomly perturbed versions of the target task instead of from itself. An information-theoretic lower bound is derived, which reveals a necessary requirement on the number of involved sources in addition to that on the number of data samples. Then, a novel HetPEVI algorithm is proposed, which simultaneously considers the sample uncertainties from a finite number of data samples per data source and the source uncertainties due to a finite number of available data sources. Theoretical analyses demonstrate that HetPEVI can solve the target task as long as the data sources collectively provide a good data coverage. Moreover, HetPEVI is demonstrated to be optimal up to a polynomial factor of the horizon length. Finally, the study is extended to offline Markov games and offline robust RL, which demonstrates the generality of the proposed designs and theoretical analyses.

Despite the significant interest and progress in reinforcement learning (RL) problems with adversarial corruption, current works are either confined to the linear setting or lead to an undesired $\tilde{\mathcal O}(\sqrt{T}\zeta)$ regret bound, where $T$ is the number of rounds and $\zeta$ is the total amount of corruption. In this paper, we consider contextual bandits with general function approximation and propose a computationally efficient algorithm to achieve a regret of $\tilde{\mathcal O}(\sqrt{T}+\zeta)$. The proposed algorithm relies on the recently developed uncertainty-weighted least-squares regression from linear contextual bandits (He et al., 2022) and a new weighted estimator of uncertainty for the general function class. In contrast to the existing analysis for the sum of uncertainty that is heavily based on the linear structure, we develop a novel technique to control the sum of weighted uncertainty, thus establishing the final regret bound. We then generalize our algorithm to the episodic MDP and first achieve an additive dependence on the corruption level $\zeta$ in the scenario of general function approximation. Notably, our algorithms achieve regret bounds that either nearly match the lower bound or improve the performance of existing methods for all the corruption levels in both known and unknown $\zeta$ cases.

Most existing federated multi-armed bandits (FMAB) designs are based on the presumption that clients will implement the new design to collaborate with the server. In reality, however, it may not be possible to modify the client protocols. Motivated by this limitation, this work focuses on clients who always maximize their individual cumulative rewards, and introduces a novel idea of reward teaching, where the server guides the clients towards global optimality through implicit local reward adjustments. Under this framework, the server faces two tightly coupled tasks of bandit learning and target teaching, whose combination is non-trivial and challenging. A novel algorithm, called Teaching-After-Learning (TAL), is proposed, which encourages and discourages clients’ explorations separately. General performance analyses of TAL on regret and cost are first established when the clients’ strategies satisfy certain requirements. To particularize the results, clients with UCB or ε-greedy strategies are then considered, where novel technical approaches are developed to analyze their warm-start behaviors. The obtained guarantees concretely demonstrate that when facing these client strategies, TAL achieves logarithmic regrets while only incurring logarithmic adjustment costs, which is order-optimal w.r.t. a natural lower bound.

In reinforcement learning (RL), balancing exploration and exploitation is crucial for achieving an optimal policy in a sample-efficient way. To this end, existing sample- efficient algorithms typically consist of three components: estimation, planning, and exploration. However, to cope with general function approximators, most of them involve impractical algorithmic components to incentivize exploration, such as data-dependent level-set constraints or complicated sampling procedures. To address this challenge, we propose an easy-to-implement RL framework called Maximize to Explore (MEX), which only needs to optimize unconstrainedly a single objective that integrates the estimation and planning components while balancing exploration and exploitation automatically. Theoretically, we prove that the MEX achieves a sublinear regret with general function approximators and is extendable to the zero-sum Markov game setting. Meanwhile, we adapt deep RL baselines to design practical versions of MEX in both the model-based and model-free settings, which outperform baselines in various MuJoCo environments with sparse reward by a stable margin. Compared with existing sample-efficient algorithms with general function approximators, MEX achieves similar sample efficiency while also enjoying a lower computational cost and is more compatible with modern deep RL methods.

Existing studies on provably efficient algorithms for Markov games (MGs) almost exclusively build on the “optimism in the face of uncertainty” (OFU) principle. This work focuses on a distinct approach of posterior sampling, which is celebrated in many bandits and reinforcement learning settings but remains under-explored for MGs. Specifically, for episodic two-player zero-sum MGs, a novel posterior sampling algorithm is developed with general function approximation. Theoretical analysis demonstrates that the posterior sampling algorithm admits a $\sqrt{T}$-regret bound for problems with a low multi-agent decoupling coefficient, which is a new complexity measure for MGs, where $T$ denotes the number of episodes. When specializing to linear MGs, the obtained regret bound matches the state-of-the-art results. To the best of our knowledge, this is the first provably efficient posterior sampling algorithm for MGs with frequentist regret guarantees, which extends the toolbox for MGs and promotes the broad applicability of posterior sampling.

We study episodic two-player zero-sum Markov games (MGs) in the offline setting, where the goal is to find an approximate Nash equilibrium (NE) policy pair based on a dataset collected a priori. When the dataset does not have uniform coverage over all policy pairs, finding an approximate NE involves challenges in three aspects: (i) distributional shift between the behavior policy and the optimal policy, (ii) function approximation to handle large state space, and (iii) minimax optimization for equilibrium solving. We propose a pessimism-based algorithm, dubbed as pessimistic minimax value iteration (PMVI), which overcomes the distributional shift by constructing pessimistic estimates of the value functions for both players and outputs a policy pair by solving a correlated coarse equilibrium based on the two value functions. Furthermore, we establish a data-dependent upper bound on the suboptimality which recovers a sublinear rate without the assumption on uniform coverage of the dataset. We also prove an information-theoretical lower bound, which shows our upper bound is nearly minimax optimal, which suggests that the data-dependent term is intrinsic. Our theoretical results also highlight a notion of “relative uncertainty”, which characterizes the necessary and sufficient condition for achieving sample efficiency in offline MGs. To the best of our knowledge, we provide the first nearly minimax optimal result for offline MGs with function approximation.

Despite the significant interests and many progresses in decentralized multi-player multi-armed bandits (MP-MAB) problems in recent years, the regret gap to the natural centralized lower bound in the heterogeneous MP-MAB setting remains open. In this paper, we propose BEACON -- Batched Exploration with Adaptive COmmunicatioN -- that closes this gap. BEACON accomplishes this goal with novel contributions in implicit communication and efficient exploration. For the former, we propose a novel adaptive differential communication (ADC) design that significantly improves the implicit communication efficiency. For the latter, a carefully crafted batched exploration scheme is developed to enable incorporation of the combinatorial upper confidence bound (CUCB) principle. We then generalize the existing linear-reward MP-MAB problems, where the system reward is always the sum of individually collected rewards, to a new MP-MAB problem where the system reward is a general (nonlinear) function of individual rewards. We extend BEACON to solve this problem and prove a logarithmic regret. BEACON bridges the algorithm design and regret analysis of combinatorial MAB (CMAB) and MP-MAB, two largely disjointed areas in MAB, and the results in this paper suggest that this previously ignored connection is worth further investigation.

Incentivized exploration in multi-armed bandits (MAB) has witnessed increasing interests and many progresses in recent years, where a principal offers bonuses to agents to do explorations on her behalf. However, almost all existing studies are confined to temporary myopic agents. In this work, we break this barrier and study incentivized exploration with multiple and long-term strategic agents, who have more complicated behaviors that often appear in real-world applications. An important observation of this work is that strategic agents' intrinsic needs of learning benefit (instead of harming) the principal's explorations by providing "free pulls". Moreover, it turns out that increasing the population of agents significantly lowers the principal's burden of incentivizing. The key and somewhat surprising insight revealed from our results is that when there are sufficiently many learning agents involved, the exploration process of the principal can be (almost) free. Our main results are built upon three novel components which may be of independent interest: (1) a simple yet provably effective incentive-provision strategy; (2) a carefully crafted best arm identification algorithm for rewards aggregated under unequal confidences; (3) a high-probability finite-time lower bound of UCB algorithms. Experimental results are provided to complement the theoretical analysis.

A growing trend for value-based reinforcement learning (RL) algorithms is to capture more information than scalar value functions in the value network. One of the most well-known methods in this branch is distributional RL, which models return distribution instead of scalar value. In another line of work, hybrid reward architectures (HRA) in RL have studied to model source-specific value functions for each source of reward, which is also shown to be beneficial in performance. To fully inherit the benefits of distributional RL and hybrid reward architectures, we introduce Multi-Dimensional Distributional DQN (MD3QN), which extends distributional RL to model the joint return distribution from multiple reward sources. As a by-product of joint distribution modeling, MD3QN can capture not only the randomness in returns for each source of reward, but also the rich reward correlation between the randomness of different sources. We prove the convergence for the joint distributional Bellman operator and build our empirical algorithm by minimizing the Maximum Mean Discrepancy between joint return distribution and its Bellman target. In experiments, our method accurately models the joint return distribution in environments with richly correlated reward functions, and outperforms previous RL methods utilizing multi-dimensional reward functions in the control setting.

The decentralized stochastic multi-player multi-armed bandit (MP-MAB) problem, where the collision information is not available to the players, is studied in this paper. Building on the seminal work of Boursier and Perchet (2019), we propose error correction synchronization involving communication (EC-SIC), whose regret is shown to approach that of the centralized stochastic MP-MAB with collision information. By recognizing that the communication phase without collision information corresponds to the Z-channel model in information theory, the proposed EC-SIC algorithm applies optimal error correction coding for the communication of reward statistics. A fixed message length, as opposed to the logarithmically growing one in Boursier and Perchet (2019), also plays a crucial role in controlling the communication loss. Experiments with practical Z-channel codes, such as repetition code, flip code and modified Hamming code, demonstrate the superiority of EC-SIC in both synthetic and real-world datasets.