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Theory · Reinforcement Learning and Planning

Kevin Tan, Wei Fan, Yuting Wei

Actor-critic algorithms have become a cornerstone in reinforcement learning (RL), leveraging the strengths of both policy-based and value-based methods. Despite recent progress in understanding their statistical efficiency, no existing work has successfully learned an $\epsilon$-optimal policy with a sample complexity of $O(1/\epsilon^2)$ trajectories with general function approximation when strategic exploration is necessary. We address this open problem by introducing a novel actor-critic algorithm that attains a sample-complexity of $O(dH^5 \log|\mathcal{A}|/\epsilon^2 + d H^4 \log|\mathcal{F}|/ \epsilon^2)$ trajectories, and accompanying $\sqrt{T}$ regret when the Bellman eluder dimension $d$ does not increase with $T$ at more than a $\log T$ rate. Here, $\mathcal{F}$ is the critic function class, and $\mathcal{A}$ is the action space. Our algorithm integrates optimism, off-policy critic estimation targeting the optimal Q-function, and rare-switching policy resets. We extend this to the setting of Hybrid RL, where we show that initializing the critic with offline data yields sample efficiency gains, and also provide a \textit{non-optimistic} provably efficient actor-critic algorithm, addressing another open problem in the literature. Numerical experiments support our theoretical findings.

Reinforcement Learning · Planning

Shuyuan Wang, Philip D. Loewen, Michael Forbes, Bhushan Gopaluni, Wei Pan

While differentiable control has emerged as a powerful paradigm combining model-free flexibility with model-based efficiency, the iterative Linear Quadratic Regulator (iLQR) remains underexplored as a differentiable component. The scalability of differentiating through extended iterations and horizons poses significant challenges, hindering iLQR from being an effective differentiable controller. This paper introduces DiLQR, a framework that facilitates differentiation through iLQR, allowing it to serve as a trainable and differentiable module, either as or within a neural network. A novel aspect of this framework is the analytical solution that it provides for the gradient of an iLQR controller through implicit differentiation, which ensures a constant backward cost regardless of iteration, while producing an accurate gradient. We evaluate our framework on imitation tasks on famous control benchmarks. Our analytical method demonstrates superior computational performance, achieving up to $\textbf{128x}$ speedup and a minimum of $\textbf{21x}$ speedup compared to automatic differentiation. Our method also demonstrates superior learning performance ($\mathbf{10^6x}$) compared to traditional neural network policies and better model loss with differentiable controllers that lack exact analytical gradients. Furthermore, we integrate our module into a larger network with visual inputs to demonstrate the capacity of our method for high-dimensional, fully end-to-end tasks. Codes can be found on the project homepage~\url{https://sites.google.com/view/dilqr/}.

Reinforcement Learning · Deep RL

Mingyang Sun, Pengxiang Ding, Weinan Zhang, Donglin Wang

Diffusion policies have shown promise in learning complex behaviors from demonstrations, particularly for tasks requiring precise control and long-term planning. However, they face challenges in robustness when encountering distribution shifts. This paper explores improving diffusion-based imitation learning models through online interactions with the environment. We propose OTPR (Optimal Transport-guided score-based diffusion Policy for Reinforcement learning fine-tuning), a novel method that integrates diffusion policies with RL using optimal transport theory. OTPR leverages the Q-function as a transport cost and views the policy as an optimal transport map, enabling efficient and stable fine-tuning. Moreover, we introduce masked optimal transport to guide state-action matching using expert keypoints and a compatibility-based resampling strategy to enhance training stability. Experiments on three simulation tasks demonstrate OTPR's superior performance and robustness compared to existing methods, especially in complex and sparse-reward environments. In sum, OTPR provides an effective framework for combining IL and RL, achieving versatile and reliable policy learning.

Reinforcement Learning · Multi-agent

Whiyoung Jung, Sunghoon Hong, Deunsol Yoon, Kanghoon Lee, Woohyung Lim

Multi-Agent Reinforcement Learning (MARL) struggles with coordination in sparse reward environments. Macro-actions —sequences of actions executed as single decisions— facilitate long-term planning but introduce asynchrony, complicating Centralized Training with Decentralized Execution (CTDE). Existing CTDE methods use padding to handle asynchrony, risking misaligned asynchronous experiences and spurious correlations. We propose the Agent-Centric Actor-Critic (ACAC) algorithm to manage asynchrony without padding. ACAC uses agent-centric encoders for independent trajectory processing, with an attention-based aggregation module integrating these histories into a centralized critic for improved temporal abstractions. The proposed structure is trained via a PPO-based algorithm with a modified Generalized Advantage Estimation for asynchronous environments. Experiments show ACAC accelerates convergence and enhances performance over baselines in complex MARL tasks.

Reinforcement Learning · Planning

Mingde Zhao, Tristan Sylvain, Romain Laroche, Doina Precup, Yoshua Bengio

Generative models can be used in planning to propose targets corresponding to states that agents deem either likely or advantageous to experience. However, imperfections, common in learned models, lead to infeasible hallucinated targets, which can cause delusional behaviors and thus safety concerns. This work first categorizes and investigates the properties of several kinds of infeasible targets. Then, we devise a strategy to reject infeasible targets with a generic target evaluator, which trains alongside planning agents as an add-on without the need to change the behavior nor the architectures of the agent (and the generative model) it is attached to. We highlight that, without proper design, the evaluator can produce delusional estimates, rendering the strategy futile. Thus, to learn correct evaluations of infeasible targets, we propose to use a combination of learning rule, architecture, and two assistive hindsight relabeling strategies. Our experiments validate significant reductions in delusional behaviors and performance improvements for several kinds of existing planning agents.

Theory · Reinforcement Learning and Planning

Heyang Zhao, Chenlu Ye, Wei Xiong, Quanquan Gu, Tong Zhang

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.

Theory · Reinforcement Learning and Planning

Uri Sherman, Tomer Koren, Yishay Mansour

Modern policy optimization methods roughly follow the policy mirror descent (PMD) algorithmic template, for which there are by now numerous theoretical convergence results. However, most of these either target tabular environments, or can be applied effectively only when the class of policies being optimized over satisfies strong closure conditions, which is typically not the case when working with parametric policy classes in large-scale environments. In this work, we develop a theoretical framework for PMD for general policy classes where we replace the closure conditions with a generally weaker variational gradient dominance assumption, and obtain upper bounds on the rate of convergence to the best-in-class policy. Our main result leverages a novel notion of smoothness with respect to a local norm induced by the occupancy measure of the current policy, and casts PMD as a particular instance of smooth non-convex optimization in non-Euclidean space.

Theory · Reinforcement Learning and Planning

Bhargav Ganguly, Yang Xu, Vaneet Aggarwal

This paper investigates the potential of quantum acceleration in addressing infinite horizon Markov Decision Processes (MDPs) to enhance average reward outcomes. We introduce an innovative quantum framework for the agent's engagement with an unknown MDP, extending the conventional interaction paradigm. Our approach involves the design of an optimism-driven tabular Reinforcement Learning algorithm that harnesses quantum signals acquired by the agent through efficient quantum mean estimation techniques. Through thorough theoretical analysis, we demonstrate that the quantum advantage in mean estimation leads to exponential advancements in regret guarantees for infinite horizon Reinforcement Learning. Specifically, the proposed Quantum algorithm achieves a regret bound of $\tilde{\mathcal{O}}(1)$\footnote{$\tilde{\mathcal{O}}(\cdot)$ conceals logarithmic terms of $T$.}, a significant improvement over the $\tilde{\mathcal{O}}(\sqrt{T})$ bound exhibited by classical counterparts, where $T$ is the length of the time horizon.

Theory · Reinforcement Learning and Planning

Qian Qi

We establish a continuous-time framework for analyzing Deep Q-Networks (DQNs) via stochastic control and Forward-Backward Stochastic Differential Equations (FBSDEs). Considering a continuous-time Markov Decision Process (MDP) driven by a square-integrable martingale, we analyze DQN approximation properties. We show that DQNs can approximate the optimal Q-function on compact sets with arbitrary accuracy and high probability, leveraging residual network approximation theorems and large deviation bounds for the state-action process. We then analyze the convergence of a general Q-learning algorithm for training DQNs in this setting, adapting stochastic approximation theorems. Our analysis emphasizes the interplay between DQN layer count, time discretization, and the role of viscosity solutions (primarily for the value function $V^*$) in addressing potential non-smoothness of the optimal Q-function. This work bridges deep reinforcement learning and stochastic control, offering insights into DQNs in continuous-time settings, relevant for applications with physical systems or high-frequency data.

Reinforcement Learning · Planning

Wenhao Zhao, Qiushui Xu, Linjie Xu, Lei Song, Jinyu Wang, Chunlai Zhou, Jiang Bian

Recently, incorporating knowledge from pretrained language models (PLMs) into decision transformers (DTs) has generated significant attention in offline reinforcement learning (RL). These PLMs perform well in RL tasks, raising an intriguing question: what kind of knowledge from PLMs has been transferred to RL to achieve such good results? This work first dives into this problem by analyzing each head quantitatively and points out Markov head, a crucial component that exists in the attention heads of PLMs. It leads to extreme attention on the last-input token and performs well only in short-term environments. Furthermore, we prove that this extreme attention cannot be changed by re-training embedding layer or fine-tuning. Inspired by our analysis, we propose a general method GPT-DTMA, which equips a pretrained DT with Mixture of Attention (MoA), to enable adaptive learning and accommodate diverse attention requirements during fine-tuning. Extensive experiments demonstrate the effectiveness of GPT-DTMA: it achieves superior performance in short-term environments compared to baselines, significantly reduces the performance gap of PLMs in long-term scenarios, and the experimental results also validate our theorems.

Theory · Reinforcement Learning and Planning

Taehyun Cho, Seungyub Han, Seokhun Ju, Dohyeong Kim, Kyungjae Lee, Jungwoo Lee

Distributional reinforcement learning improves performance by capturing environmental stochasticity, but a comprehensive theoretical understanding of its effectiveness remains elusive.In addition, the intractable element of the infinite dimensionality of distributions has been overlooked.In this paper, we present a regret analysis of distributional reinforcement learning with general value function approximation in a finite episodic Markov decision process setting. We first introduce a key notion of Bellman unbiasedness which is essential for exactly learnable and provably efficient distributional updates in an online manner.Among all types of statistical functionals for representing infinite-dimensional return distributions, our theoretical results demonstrate that only moment functionals can exactly capture the statistical information.Secondly, we propose a provably efficient algorithm, SF-LSVI, that achieves a tight regret bound of $\tilde{O}(d_E H^{\frac{3}{2}}\sqrt{K})$ where $H$ is the horizon, $K$ is the number of episodes, and $d_E$ is the eluder dimension of a function class.

Theory · Reinforcement Learning and Planning

Audrey Huang, Adam Block, Qinghua Liu, Nan Jiang, Akshay Krishnamurthy, Dylan Foster

Recent work on inference-time alignment has established benefits of increasing inference-time computation in language models, but naively scaling compute through techniques like Best-of-N sampling can cause performance to degrade due to reward hacking. Toward a theoretical understanding of how to best leverage additional computation, we formalize inference-time alignment as improving a pre-trained policy’s responses for a prompt of interest, given access to an imperfect reward model. We analyze the performance of inference-time alignment algorithms in terms of (i) response quality, and (ii) compute, and provide new results that highlight the importance of the pre-trained policy’s coverage over high-quality responses for performance and compute scaling: (1) We show that Best-of-N alignment with an ideal N can achieve optimal performance under stringent notions of coverage, but provably suffers from reward hacking when N is large, and fails to achieve tight guarantees under more realistic coverage conditions; (2) We introduce InferenceTimePessimism, a new algorithm which mitigates reward hacking through deliberate use of inference-time compute, implementing pessimism in the face of uncertainty; we prove that its performance is optimal and scaling-monotonic, i.e., does ot degrade as N increases. We complement our theoretical results with experiments that demonstrate the practicality of our algorithm across a variety of tasks and models.

Theory · Reinforcement Learning and Planning

Simone Drago, Marco Mussi, Alberto Maria Metelli

The success of sequential decision-making approaches, such as *reinforcement learning* (RL), is closely tied to the availability of a reward feedback. However, designing a reward function that encodes the desired objective is a challenging task. In this work, we address a more realistic scenario: sequential decision making with preference feedback provided, for instance, by a human expert. We aim to build a theoretical basis linking *preferences*, (non-Markovian) *utilities*, and (Markovian) *rewards*, and we study the connections between them. First, we model preference feedback using a partial (pre)order over trajectories, enabling the presence of incomparabilities that are common when preferences are provided by humans but are surprisingly overlooked in existing works. Second, to provide a theoretical justification for a common practice, we investigate how a preference relation can be approximated by a multi-objective utility. We introduce a notion of preference-utility compatibility and analyze the computational complexity of this transformation, showing that constructing the minimum-dimensional utility is NP-hard. Third, we propose a novel concept of preference-based policy dominance that does not rely on utilities or rewards and discuss the computational complexity of assessing it. Fourth, we develop a computationally efficient algorithm to approximate a utility using (Markovian) rewards and quantify the error in terms of the suboptimality of the optimal policy induced by the approximating reward. This work aims to lay the foundation for a principled approach to sequential decision making from preference feedback, with promising potential applications in RL from human feedback.

Reinforcement Learning · Batch/Offline

Haofei Lu, Yifei Shen, Dongsheng Li, Junliang Xing, Dongqi Han

Diffusion models have shown great promise in decision-making, also known as diffusion planning. However, the slow inference speeds limit their potential for broader real-world applications. Here, we introduce **Habi**, a general framework that transforms powerful but slow diffusion planning models into fast decision-making models, which mimics the cognitive process in the brain that costly goal-directed behavior gradually transitions to efficient habitual behavior with repetitive practice. Even using a laptop CPU, the habitized model can achieve an average **800+ Hz** decision-making frequency (faster than previous diffusion planners by orders of magnitude) on standard offline reinforcement learning benchmarks D4RL, while maintaining comparable or even higher performance compared to its corresponding diffusion planner. Our work proposes a fresh perspective of leveraging powerful diffusion models for real-world decision-making tasks. We also provide robust evaluations and analysis, offering insights from both biological and engineering perspectives for efficient and effective decision-making.

Reinforcement Learning · Planning

Aidan Curtis, Eric Li, Michael S Noseworthy, Nishad Gothoskar, Sachin Chitta, Hui Li, Leslie Kaelbling, Nicole Carey

Domain randomization in reinforcement learning is an established technique for increasing the robustness of control policies learned in simulation. By randomizing properties of the environment during training, the learned policy can be robust to uncertainty along the randomized dimensions. While the environment distribution is typically specified by hand, in this paper we investigate the problem of automatically discovering this sampling distribution via entropy-regularized reward maximization of a neural sampling distribution in the form of a normalizing flow. We show that this architecture is more flexible and results in better robustness than existing approaches to learning simple parameterized sampling distributions. We demonstrate that these policies can be used to learn robust policies for contact-rich assembly tasks. Additionally, we explore how these sampling distributions, in combination with a privileged value function, can be used for out-of-distribution detection in the context of an uncertainty-aware multi-step manipulation planner.

Reinforcement Learning · Multi-agent

Mason O. Smith, Wenlong Zhang

Humans are often modeled as rational actors by interactive agents when they are in fact frequently observed to make biased decisions. This erroneous assumption may cause an agent’s model of the human to fail, especially when interaction occurs in bias-inducing settings that prompt risky decisions. To address this, this paper formulates a risk-sensitive multi-agent coordination problem and presents the novel Risk-Sensitive Theory of Mind (RS-ToM) framework that allows an autonomous agent to reason about and adapt to a partner of unknown risk-sensitivity. In simulated studies, we show that an agent with an RS-ToM is able to better coordinate with such a partner when compared to an agent that assumes their partner is rational. Thus, we observe significant improvements to team performance, coordination fluency, compliance with partner risk-preferences, and predictability. The presented results suggest that an RS-ToM will be able to model and plan with partners that exhibit these risk-sensitive biases in the real world.

Theory · Reinforcement Learning and Planning

Chenbei Lu, Laixi Shi, Zaiwei Chen, Chenye Wu, Adam Wierman

Factored Markov Decision Processes (FMDPs) offer a promising framework for overcoming the curse of dimensionality in reinforcement learning (RL) by decomposing high-dimensional MDPs into smaller and independently evolving components. Despite their potential, existing studies on FMDPs face three key limitations: reliance on perfectly factorizable models, suboptimal sample complexity guarantees for model-based algorithms, and the absence of model-free algorithms. To address these challenges, we introduce approximate factorization, which extends FMDPs to handle imperfectly factored models. Moreover, we develop a model-based algorithm and a model-free algorithm (in the form of variance-reduced Q-learning), both achieving the first near-minimax sample complexity guarantees for FMDPs. A key novelty in the design of these two algorithms is the development of a graph-coloring-based optimal synchronous sampling strategy. Numerical simulations based on the wind farm storage control problem corroborate our theoretical findings.

Deep Learning · Large Language Models

Ziliang Chen, Zhao-Rong Lai, Yufeng Yang, Liangda Fang, ZHANFU YANG, Liang Lin

Despite advancing language model (LM) alignment, direct preference optimization (DPO) falls short in LM reasoning with the free lunch from reinforcement learning (RL). As the breakthrough, this work proposes a new RL-free preference optimization method aiming to achieve DPO along with learning another LM, whose response generation policy holds the asymptotic equivalence with AlphaZero-like search, the apex of algorithms for complex reasoning missions like chess Go. While circumventing explicit value and reward modeling, the neural implicit tree search executed by the extra LM remains seeking to equip DPO with reasoning procedure technically akin to AlphaZero. Our experiments demonstrate that our methodology outperforms both regular DPO variants in human preference alignment, and MCTS-based LMs in mathematical reasoning and planning tasks.

Theory · Reinforcement Learning and Planning

Tong Yang, Bo Dai, Lin Xiao, Yuejie Chi

Multi-agent reinforcement learning (MARL) lies at the heart of a plethora of applications involving the interaction of a group of agents in a shared unknown environment. A prominent framework for studying MARL is Markov games, with the goal of finding various notions of equilibria in a sample-efficient manner, such as the Nash equilibrium (NE) and the coarse correlated equilibrium (CCE). However, existing sample-efficient approaches either require tailored uncertainty estimation under function approximation, or careful coordination of the players. In this paper, we propose a novel model-based algorithm, called VMG, that incentivizes exploration via biasing the empiricalestimate of the model parameters towards those with a higher collective best-response values of all the players when fixing the other players' policies, thus encouraging the policy to deviate from its current equilibrium for more exploration. VMG is oblivious to different forms of function approximation, and permits simultaneous and uncoupled policy updates of all players. Theoretically, we also establish that VMG achieves a near-optimal regret for finding both the NEs of two-player zero-sum Markov games and CCEs of multi-player general-sum Markov games under linear function approximation in an online environment, which nearly match their counterparts with sophisticated uncertainty quantification.

Theory · Reinforcement Learning and Planning

Jonathan Richens, Tom Everitt, David Abel

Are world models a necessary ingredient for flexible, goal-directed behaviour, or is model-free learning sufficient?We provide a formal answer to this question, showing that any agent capable of generalizing to multi-step goal-directed tasks must have learned a predictive model of its environment.We show that this model can be extracted from the agent's policy, and that increasing the agents performance or the complexity of the goals it can achieve requires learning increasingly accurate world models.This has a number of consequences: from developing safe and general agents, to bounding agent capabilities in complex environments, and providing new algorithms for eliciting world models from agents.