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Deep Learning · Large Language Models

Yang Li

Despite their remarkable capabilities, large language models often struggle with tasks requiring complex reasoning and planning. While existing approaches like Chain-of-Thought prompting and tree search techniques show promise, they are limited by their reliance on predefined heuristics and computationally expensive exploration strategies. We propose Policy-Guided Tree Search (PGTS), a framework that combines reinforcement learning with structured tree exploration to efficiently navigate reasoning paths. Our key innovation is a learned policy that dynamically decides between expanding, branching, backtracking, or terminating exploration, eliminating the need for manual heuristics or exhaustive search. Experiments across mathematical reasoning, logical deduction, and planning benchmarks demonstrate that PGTS achieves superior reasoning performance while significantly reducing computational costs compared to existing methods. These results establish PGTS as a scalable and effective solution for tackling complex reasoning tasks with LLMs.

Reinforcement Learning · Planning

Joery de Vries, Jinke He, Yaniv Oren, Matthijs T. J. Spaan

Monte-Carlo tree search (MCTS) has driven many recent breakthroughs in deep reinforcement learning (RL).However, scaling MCTS to parallel compute has proven challenging in practice which has motivated alternative planners like sequential Monte-Carlo (SMC). Many of these SMC methods adopt particle filters for smoothing through a reformulation of RL as a policy inference problem.Yet, persisting design choices of these particle filters often conflict with the aim of online planning in RL, which is to obtain a policy improvement at the start of planning.Drawing inspiration from MCTS, we tailor SMC planners specifically to RL by improving data generation within the planner through constrained action sampling and explicit terminal state handling, as well as improving policy and value target estimation.This leads to our *Trust-Region Twisted* SMC (TRT-SMC), which shows improved runtime and sample-efficiency over baseline MCTS and SMC methods in both discrete and continuous domains.

Theory · Reinforcement Learning and Planning

Yang Xu, Vaneet Aggarwal

We address the problem of quantum reinforcement learning (QRL) under model-free settings with quantum oracle access to the Markov Decision Process (MDP). This paper introduces a Quantum Natural Policy Gradient (QNPG) algorithm, which replaces the random sampling used in classical Natural Policy Gradient (NPG) estimators with a deterministic gradient estimation approach, enabling seamless integration into quantum systems. While this modification introduces a bounded bias in the estimator, the bias decays exponentially with increasing truncation levels. This paper demonstrates that the proposed QNPG algorithm achieves a sample complexity of $\tilde{\mathcal{O}}(\epsilon^{-1.5})$ for queries to the quantum oracle, significantly improving the classical lower bound of $\tilde{\mathcal{O}}(\epsilon^{-2})$ for queries to the MDP.

Reinforcement Learning · Planning

Jake Tuero, Michael Buro, Levi Lelis

Policy tree search is a family of tree search algorithms that use a policy to guide the search. These algorithms provide guarantees on the number of expansions required to solve a given problem that are based on the quality of the policy. While these algorithms have shown promising results, the process in which they are trained requires complete solution trajectories to train the policy. Search trajectories are obtained during a trial-and-error search process. When the training problem instances are hard, learning can be prohibitively costly, especially when starting from a randomly initialized policy. As a result, search samples are wasted in failed attempts to solve these hard instances. This paper introduces a novel method for learning subgoal-based policies for policy tree search algorithms. The subgoals and policies conditioned on subgoals are learned from the trees that the search expands while attempting to solve problems, including the search trees of failed attempts. We empirically show that our policy formulation and training method improve the sample efficiency of learning a policy and heuristic function in this online setting.

Theory · Reinforcement Learning and Planning

Gaspard Lambrechts, Damien Ernst, Aditya Mahajan

In reinforcement learning for partially observable environments, many successful algorithms have been developed within the asymmetric learning paradigm. This paradigm leverages additional state information available at training time for faster learning. Although the proposed learning objectives are usually theoretically sound, these methods still lack a precise theoretical justification for their potential benefits. We propose such a justification for asymmetric actor-critic algorithms with linear function approximators by adapting a finite-time convergence analysis to this setting. The resulting finite-time bound reveals that the asymmetric critic eliminates error terms arising from aliasing in the agent state.

Reinforcement Learning · Planning

Kyowoon Lee, Jaesik Choi

Recent advances in diffusion-based generative modeling have demonstrated significant promise in tackling long-horizon, sparse-reward tasks by leveraging offline datasets. While these approaches have achieved promising results, their reliability remains inconsistent due to the inherent stochastic risk of producing infeasible trajectories, limiting their applicability in safety-critical applications. We identify that the primary cause of these failures is inaccurate guidance during the sampling procedure, and demonstrate the existence of manifold deviation by deriving a lower bound on the guidance gap. To address this challenge, we propose *Local Manifold Approximation and Projection* (LoMAP), a *training-free* method that projects the guided sample onto a low-rank subspace approximated from offline datasets, preventing infeasible trajectory generation. We validate our approach on standard offline reinforcement learning benchmarks that involve challenging long-horizon planning. Furthermore, we show that, as a standalone module, LoMAP can be incorporated into the hierarchical diffusion planner, providing further performance enhancements.

Theory · Reinforcement Learning and Planning

Jiawei Huang, Bingcong Li, Christoph Dann, Niao He

Sample efficiency is critical for online Reinforcement Learning from Human Feedback (RLHF). While existing works investigate sample-efficient online exploration strategies, the potential of utilizing misspecified yet relevant reward models to accelerate learning remains underexplored. This paper studies how to transfer knowledge from those imperfect reward models in online RLHF. We start by identifying a novel property due to KL-regularization in the RLHF objective: \emph{a policy's coverability of the optimal policy is captured by its sub-optimality}. Building on this insight, we propose novel transfer learning principles and a theoretical algorithm---**T**ransfer **P**olicy **O**ptimization (**TPO**)---with provable benefits compared to standard online learning. Empirically, inspired by our theoretical findings, we develop a win-rate-based transfer policy selection strategy with improved computational efficiency. Moreover, our empirical transfer learning technique is modular and can be integrated with various policy optimization methods, such as DPO, IPO and XPO, to further enhance their performance. We validate the effectiveness of our method through experiments on summarization tasks.

Theory · Reinforcement Learning and Planning

Yilei Chen, Aldo Pacchiano, Ioannis Paschalidis

We study the multiple-policy evaluation problem where we are given a set of $K$ policies and the goal is to evaluate their performance (expected total reward over a fixed horizon) to an accuracy $\epsilon$ with probability at least $1-\delta$. We propose an algorithm named CAESAR for this problem. Our approach is based on computing an approximately optimal sampling distribution and using the data sampled from it to perform the simultaneous estimation of the policy values. CAESAR has two phases. In the first phase, we produce coarse estimates of the visitation distributions of the target policies at a low order sample complexity rate that scales with $\tilde{O}(\frac{1}{\epsilon})$. In the second phase, we approximate the optimal sampling distribution and compute the importance weighting ratios for all target policies by minimizing a step-wise quadratic loss function inspired by the DualDICE objective. Up to low order and logarithmic terms CAESAR achieves a sample complexity $\tilde{O}\left(\frac{H^4}{\epsilon^2}\sum_{h=1}^H\max_{k\in[K]}\sum_{s,a}\frac{(d_h^{\pi^k}(s,a))^2}{\mu^*_h(s,a)}\right)$, where $d^{\pi}$ is the visitation distribution of policy $\pi$, $\mu^*$ is the optimal sampling distribution, and $H$ is the horizon.

Theory · Reinforcement Learning and Planning

Zeyu Jia, Alexander Rakhlin, Tengyang Xie

Process and outcome supervision represent two fundamental approaches to reinforcement learning, especially for complex reasoning tasks in large language models. While process supervision offers intuitive advantages for long-term credit assignment, the precise relationship between these paradigms has remained an open question. Conventional wisdom suggests that outcome supervision is fundamentally more challenging due to the trajectory-level coverage problem, leading to significant investment in collecting fine-grained process supervision data.In this paper, we provide a possible theoretical resolution to this debate. Perhaps surprisingly, our main theorem shows that: *under standard data coverage assumptions, reinforcement learning through outcome supervision is no more statistically difficult than through process supervision*. At the core of this result lies the novel *Change of Trajectory Measure Lemma*---a powerful technical tool that bridges return-based trajectory measure and step-level distribution shift. Furthermore, for settings with access to a verifier or a rollout capability, we prove that any policy's advantage function can serve as an optimal process reward model, providing a simple yet powerful connection between outcome and process supervision. These findings suggest that the empirically observed performance gap between outcome and process supervision likely stems from algorithmic limitations rather than inherent statistical difficulties, potentially transforming how we approach data and algorithm design for reinforcement learning.

Theory · Reinforcement Learning and Planning

Kihyuk Hong, Ambuj Tewari

We study reinforcement learning in infinite-horizon average-reward settings with linear MDPs. Previous work addresses this problem by approximating the average-reward setting by discounted setting and employing a value iteration-based algorithm that uses clipping to constrain the span of the value function for improved statistical efficiency. However, the clipping procedure requires computing the minimum of the value function over the entire state space, which is prohibitive since the state space in linear MDP setting can be large or even infinite. In this paper, we introduce a value iteration method with efficient clipping operation that only requires computing the minimum of value functions over the set of states visited by the algorithm. Our algorithm enjoys the same regret bound as the previous work while being computationally efficient, with computational complexity that is independent of the size of the state space.

Theory · Reinforcement Learning and Planning

Jeremy McMahan

We study the computational complexity of approximating general constrained Markov decision processes. Our primary contribution is the design of a polynomial time $(0,\epsilon)$-additive bicriteria approximation algorithm for finding optimal constrained policies across a broad class of recursively computable constraints, including almost-sure, chance, expectation, and their anytime variants. Matching lower bounds imply our approximation guarantees are optimal so long as $P \neq NP$. The generality of our approach results in answers to several long-standing open complexity questions in the constrained reinforcement learning literature. Specifically, we are the first to prove polynomial-time approximability for the following settings: policies under chance constraints, deterministic policies under multiple expectation constraints, policies under non-homogeneous constraints (i.e., constraints of different types), and policies under constraints for continuous-state processes.

Reinforcement Learning · Multi-agent

Cassidy Laidlaw, Eli Bronstein, Timothy Guo, Dylan Feng, Lukas Berglund, Justin Svegliato, Stuart Russell, Anca Dragan

Assistance games are a promising alternative to reinforcement learning from human feedback (RLHF) for training AI assistants. Assistance games resolve key drawbacks of RLHF, such as incentives for deceptive behavior, by explicitly modeling the interaction between assistant and user as a two-player game where the assistant cannot observe their shared goal. Despite their potential, assistance games have only been explored in simple settings. Scaling them to more complex environments is difficult because it requires both solving intractable decision-making problems under uncertainty and accurately modeling human users' behavior. We present the first scalable approach to solving assistance games and apply it to a new, challenging Minecraft-based assistance game with over $10^{400}$ possible goals. Our approach, AssistanceZero, extends AlphaZero with a neural network that predicts human actions and rewards, enabling it to plan under uncertainty. We show that AssistanceZero outperforms model-free RL algorithms and imitation learning in the Minecraft-based assistance game. In a human study, our AssistanceZero-trained assistant significantly reduces the number of actions participants take to complete building tasks in Minecraft. Our results suggest that assistance games are a tractable framework for training effective AI assistants in complex environments. Code and videos are available at https://anonymous.4open.science/w/scalably-solving-assistance-games/.

Reinforcement Learning · Planning

Jaesik Yoon, Hyeonseo Cho, Doojin Baek, Yoshua Bengio, Sungjin Ahn

Diffusion models have recently emerged as a powerful tool for planning. However, unlike Monte Carlo Tree Search (MCTS)—whose performance naturally improves with inference-time computation scaling—standard diffusion‐based planners offer only limited avenues for the scalability. In this paper, we introduce Monte Carlo Tree Diffusion (MCTD), a novel framework that integrates the generative strength of diffusion models with the adaptive search capabilities of MCTS. Our method reconceptualizes denoising as a tree‐structured process, allowing partially denoised plans to be iteratively evaluated, pruned, and refined. By selectively expanding promising trajectories while retaining the flexibility to revisit and improve suboptimal branches, MCTD achieves the benefits of MCTS such as controlling exploration-exploitation trade-offs within the diffusion framework. Empirical results on challenging long‐horizon tasks show that MCTD outperforms diffusion baselines, yielding higher‐quality solutions as inference-time computation increases.

Deep Learning · Large Language Models

Yi Xie, Zhanke Zhou, Chentao Cao, Qiyu Niu, Tongliang Liu, Bo Han

Multi-agent frameworks can substantially boost the reasoning power of large language models (LLMs), but they typically incur heavy computational costs and lack convergence guarantees. To overcome these challenges, we recast multi-LLM coordination as an incomplete-information game and seek a Bayesian Nash equilibrium (BNE), in which each agent optimally responds to its probabilistic beliefs about the strategies of others. We introduce Efficient Coordination via Nash Equilibrium (ECON), a hierarchical reinforcement-learning paradigm that marries distributed reasoning with centralized final output. Under ECON, each LLM independently selects responses that maximize its expected reward, conditioned on its beliefs about co-agents, without requiring costly inter-agent exchanges.We mathematically prove that ECON attains a markedly tighter regret bound than non-equilibrium multi-agent schemes. Empirically, ECON outperforms existing multi-LLM approaches by 11.2% on average across six benchmarks spanning complex reasoning and planning tasks. Further experiments demonstrate ECON’s ability to flexibly incorporate additional models, confirming its scalability and paving the way toward larger, more powerful multi-LLM ensembles. The code is publicly available at: https://github.com/tmlr-group/ECON.

Theory · Reinforcement Learning and Planning

Zhiyong Wang, Chen Yang, John C. S. Lui, Dongruo Zhou

In this work, we study offline reinforcement learning (RL) with zero-shot generalization property (ZSG), where the agent has access to an offline dataset including experiences from different environments, and the goal of the agent is to train a policy over the training environments which performs well on test environments without further interaction. Existing work showed that classical offline RL fails to generalize to new, unseen environments. We propose pessimistic empirical risk minimization (PERM) and pessimistic proximal policy optimization (PPPO), which leverage pessimistic policy evaluation to guide policy learning and enhance generalization. We show that both PERM and PPPO are capable of finding a near-optimal policy with ZSG. Our result serves as a first step in understanding the foundation of the generalization phenomenon in offline reinforcement learning.

Theory · Reinforcement Learning and Planning

Tal Lancewicki, Yishay Mansour

We study online finite-horizon Markov Decision Processes with adversarially changing loss and aggregate bandit feedback (a.k.a full-bandit). Under this type of feedback, the agent observes only the total loss incurred over the entire trajectory, rather than the individual losses at each intermediate step within the trajectory. We introduce the first Policy Optimization algorithms for this setting. In the known-dynamics case, we achieve the first *optimal* regret bound of $\tilde \Theta(H^2\sqrt{SAK})$, where $K$ is the number of episodes, $H$ is the episode horizon, $S$ is the number of states, and $A$ is the number of actions. In the unknown dynamics case we establish regret bound of $\tilde O(H^3 S \sqrt{AK})$, significantly improving the best known result by a factor of $H^2 S^5 A^2$.

Theory · Reinforcement Learning and Planning

Jongmin Lee, Mario Bravo, Roberto Cominetti

We study a new model-free algorithm to compute $\varepsilon$-optimal policies for average reward Markov decision processes, in the weakly communicating setting. Given a generative model, our procedure combines a recursive sampling technique with Halpern's anchored iteration, and computes an $\varepsilon$-optimal policy with sample and time complexity $\widetilde{O}(|\mathcal{S}||\mathcal{A}|\||h\||^{2}/\varepsilon^{2})$ both in high probability and in expectation. To our knowledge, this is the best complexity among model-free algorithms, matching the known lower bound up to a factor $ \||h\|| $. Although the complexity bound involves the span seminorm $ \||h\|| $ of the unknown bias vector, the algorithm requires no prior knowledge and implements a stopping rule which guarantees with probability 1 that the procedure terminates in finite time. We also analyze how these techniques can be adapted for discounted MDPs.

Theory · Reinforcement Learning and Planning

Hongyi Zhou, Josiah Hanna, Jin Zhu, Ying Yang, Chengchun Shi

This paper studies off-policy evaluation (OPE) in reinforcement learning with a focus on behavior policy estimation for importance sampling. Prior work has shown empirically that estimating a history-dependent behavior policy can lead to lower mean squared error (MSE) even when the true behavior policy is Markovian. However, the question of *why* the use of history should lower MSE remains open. In this paper, we theoretically demystify this paradox by deriving a bias-variance decomposition of the MSE of ordinary importance sampling (IS) estimators, demonstrating that history-dependent behavior policy estimation decreases their asymptotic variances while increasing their finite-sample biases. Additionally, as the estimated behavior policy conditions on a longer history, we show a consistent decrease in variance. We extend these findings to a range of other OPE estimators, including the sequential IS estimator, the doubly robust estimator and the marginalized IS estimator, with the behavior policy estimated either parametrically or non-parametrically.

Theory · Reinforcement Learning and Planning

Xinyu Liu, Zixuan Xie, Shangtong Zhang

$Q$-learning is one of the most fundamental reinforcement learning algorithms.It is widely believed that $Q$-learning with linear function approximation (i.e., linear $Q$-learning) suffers from possible divergence until the recent work Meyn (2024) which establishes the ultimate almost sure boundedness of the iterates of linear $Q$-learning.Building on this success,this paper further establishes the first $L^2$ convergence rate of linear $Q$-learning iterates (to a bounded set).Similar to Meyn (2024),we do not make any modification to the original linear $Q$-learning algorithm, do not make any Bellman completeness assumption,and do not make any near-optimality assumption on the behavior policy.All we need is an $\epsilon$-softmax behavior policy with an adaptive temperature.The key to our analysis is the general result of stochastic approximations under Markovian noise with fast-changing transition functions.As a side product,we also use this general result to establish the $L^2$ convergence rate of tabular $Q$-learning with an $\epsilon$-softmax behavior policy,for which we rely on a novel pseudo-contraction property of the weighted Bellman optimality operator.

Reinforcement Learning · Planning

Cheol Kim, Jai Moondra, Shresth Verma, Madeleine Pollack, Lingkai Kong, Milind Tambe, Swati Gupta

In many real-world applications of Reinforcement Learning (RL), deployed policies have varied impacts on different stakeholders, creating challenges in reaching consensus on how to effectively aggregate their preferences. Generalized $p$-means form a widely used class of social welfare functions for this purpose, with broad applications in fair resource allocation, AI alignment, and decision-making. This class includes well-known welfare functions such as Egalitarian, Nash, and Utilitarian welfare. However, selecting the appropriate social welfare function is challenging for decision-makers, as the structure and outcomes of optimal policies can be highly sensitive to the choice of $p$. To address this challenge, we study the concept of an $\alpha$-approximate portfolio in RL, a set of policies that are approximately optimal across the family of generalized $p$-means for all $p \in [-\infty, 1]$. We propose algorithms to compute such portfolios and provide theoretical guarantees on the trade-offs among approximation factor, portfolio size, and computational efficiency. Experimental results on synthetic and real-world datasets demonstrate the effectiveness of our approach in summarizing the policy space induced by varying $p$ values, empowering decision-makers to navigate this landscape more effectively.