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Theory · Reinforcement Learning and Planning

Swetha Ganesh, Vaneet Aggarwal

Actor-Critic methods are widely used for their scalability, yet existing theoretical guarantees for infinite-horizon average-reward Markov Decision Processes (MDPs) often rely on restrictive ergodicity assumptions. We propose NAC-B, a Natural Actor-Critic with Batching, that achieves order-optimal regret of \$\tilde{O}(\sqrt{T})\$ in infinite-horizon average-reward MDPs under the unichain assumption, which permits both transient states and periodicity. This assumption is among the weakest under which the classic policy gradient theorem remains valid for average-reward settings. NAC-B employs function approximation for both the actor and the critic, enabling scalability to problems with large state and action spaces. The use of batching in our algorithm helps mitigate potential periodicity in the MDP and reduces stochasticity in gradient estimates, and our analysis formalizes these benefits through the introduction of the constants $C_{\text{hit}}$ and $C_{\text{tar}}$, which characterize the rate at which empirical averages over Markovian samples converge to the stationary distribution.

Theory · Reinforcement Learning and Planning

Weikai Wang, Erick Delage

For continuing tasks, average cost Markov decision processes have well-documented value and can be solved using efficient algorithms. However, it explicitly assumes that the agent is risk-neutral. In this work, we extend risk-neutral algorithms to accommodate the more general class of dynamic risk measures. Specifically, we propose a relative value iteration (RVI) algorithm for planning and design two model-free Q-learning algorithms, namely a generic algorithm based on the multi-level Monte Carlo (MLMC) method, and an off-policy algorithm dedicated to utility-based shortfall risk measures. Both the RVI and MLMC-based Q-learning algorithms are proven to converge to optimality. Numerical experiments validate our analysis, confirm empirically the convergence of the off-policy algorithm, and demonstrate that our approach enables the identification of policies that are finely tuned to the intricate risk-awareness of the agent that they serve.

Applications · Neuroscience, Cognitive Science

Sounak Banerjee, Daphne Cornelisse, Deepak Gopinath, Emily Sumner, Jonathan DeCastro, Guy Rosman, Eugene Vinitsky, Mark Ho

People's goal-directed behaviors are influenced by their cognitive biases, and autonomous systems that interact with people should be aware of this. For example, people's attention to objects in their environment will be biased in a way that systematically affects how they perform everyday tasks such as driving to work. Here, building on recent work in computational cognitive science, we formally articulate the \textit{attention-aware inverse planning problem}, in which the goal is to estimate a person's attentional biases from their actions. We demonstrate how attention-aware inverse planning systematically differs from standard inverse reinforcement learning and how cognitive biases can be inferred from behavior. Finally, we present an approach to attention-aware inverse planning that combines deep reinforcement learning with computational cognitive modeling. We use this approach to infer the attentional strategies of RL agents in real-life driving scenarios selected from the Waymo Open Dataset, demonstrating the scalability of estimating cognitive biases with attention-aware inverse planning.

Theory · Reinforcement Learning and Planning

Jifeng Hu, Sili Huang, Zhejian Yang, Shengchao Hu, Li Shen, Hechang Chen, Lichao Sun, Yi Chang, Dacheng Tao

Conditional decision generation with diffusion models has shown powerful competitiveness in reinforcement learning (RL). Recent studies reveal the relation between energy-function-guidance diffusion models and constrained RL problems. The main challenge lies in estimating the intermediate energy, which is intractable due to the log-expectation formulation during the generation process. To address this issue, we propose the Analytic Energy-guided Policy Optimization (AEPO). Specifically, we first provide a theoretical analysis and the closed-form solution of the intermediate guidance when the diffusion model obeys the conditional Gaussian transformation. Then, we analyze the posterior Gaussian distribution in the log-expectation formulation and obtain the target estimation of the log-expectation under mild assumptions. Finally, we train an intermediate energy neural network to approach the target estimation of log-expectation formulation. We apply our method in 30+ offline RL tasks to demonstrate the effectiveness of our method. Extensive experiments illustrate that our method surpasses numerous representative baselines in D4RL offline reinforcement learning benchmarks.

Optimization

Hongshu Guo, Zeyuan Ma, Yining Ma, Xinglin Zhang, Wei-Neng Chen, Yue-Jiao Gong

Designing effective black‑box optimizers is hampered by limited problem-specific knowledge and manual control that spans months for almost every detail. In this paper, we present DesignX, the first automated algorithm design framework that generates an effective optimizer specific to a given black-box optimization problem within seconds. Rooted in the first principles, we identify two key sub-tasks: 1) algorithm structure generation and 2) hyperparameter control. To enable systematic construction, a comprehensive modular algorithmic space is first built, embracing hundreds of algorithm components collected from decades of research. We then introduce a dual-agent reinforcement learning system that collaborates on structural and parametric design through a novel cooperative training objective, enabling large-scale meta-training across 10k diverse instances. Remarkably, through days of autonomous learning, the DesignX-generated optimizers continuously surpass human-crafted optimizers by orders of magnitude, either on synthetic testbed or on realistic optimization scenarios such as Protein-docking, AutoML and UAV path planning. Further in-depth analysis reveals DesignX's capability to discover non-trivial algorithm patterns beyond expert intuition, which, conversely, provides valuable design insights for the optimization community. We provide DesignX's Python project at~\url{https://github.com/MetaEvo/DesignX}.

Theory · Reinforcement Learning and Planning

Hao Liang, Zhiquan Luo

We study the regret guarantee for risk-sensitive reinforcement learning (RSRL) via distributional reinforcement learning (DRL) methods. In particular, we consider finite episodic Markov decision processes whose objective is the entropic risk measure (EntRM) of return. By leveraging a key property of the EntRM, the independence property, we establish the risk-sensitive distributional dynamic programming framework. We then propose two novel DRL algorithms that implement optimism through two different schemes, including a model-free one and a model-based one. We prove that they both attain $\tilde{\mathcal{O}}\left(\frac{\exp(|\beta| H)-1}{|\beta|}H\sqrt{S^2AK}\right)$ regret upper bound, where $S$, $A$, $K$, $H$, $T=KH$, and $\beta$ represent the number of states, actions, episodes, time horizon, number of total time-steps, and risk parameter respectively. It matches RSVI2, with novel distributional analysis that focuses on the distributions of returns rather than the risk values associated with these returns. To the best of our knowledge, this is the first regret analysis that bridges DRL and RSRL in terms of sample complexity. To address the computational inefficiencies inherent in the model-free DRL algorithm, we propose an alternative DRL algorithm with distribution representation. This approach effectively represents any bounded distribution using a refined distribution class. It significantly amplifies computational efficiency while maintaining the established regret bounds.We also prove a tighter minimax lower bound of $\Omega\left(\frac{\exp(\beta H/6)-1}{\beta }\sqrt{SAT}\right)$ for the $\beta>0$ case, which recovers the tight lower bound $\Omega(H\sqrt{SAT})$ in the risk-neutral setting.

Theory · Reinforcement Learning and Planning

Yu-Jie Zhang, Sheng-An Xu, Peng Zhao, Masashi Sugiyama

We study the generalized linear bandit (GLB) problem, a contextual multi-armed bandit framework that extends the classical linear model by incorporating a non-linear link function, thereby modeling a broad class of reward distributions such as Bernoulli and Poisson. While GLBs are widely applicable to real-world scenarios, their non-linear nature introduces significant challenges in achieving both computational and statistical efficiency. Existing methods typically trade off between two objectives, either incurring high per-round costs for optimal regret guarantees or compromising statistical efficiency to enable constant-time updates. In this paper, we propose a jointly efficient algorithm that attains a nearly optimal regret bound with $\mathcal{O}(1)$ time and space complexities per round. The core of our method is a tight confidence set for the online mirror descent (OMD) estimator, which is derived through a novel analysis that leverages the notion of mix loss from online prediction. The analysis shows that our OMD estimator, even with its one-pass updates, achieves statistical efficiency comparable to maximum likelihood estimation, thereby leading to a jointly efficient optimistic method.

Theory · Reinforcement Learning and Planning

Shinji Ito, Kevin Jamieson, Haipeng Luo, Arnab Maiti, Taira Tsuchiya

We study online learning in finite-horizon episodic Markov decision processes (MDPs) under the challenging \textit{aggregate bandit feedback} model, where the learner observes only the cumulative loss incurred in each episode, rather than individual losses at each state-action pair. While prior work in this setting has focused exclusively on worst-case analysis, we initiate the study of \textit{best-of-both-worlds} (BOBW) algorithms that achieve low regret in both stochastic and adversarial environments. We propose the first BOBW algorithms for episodic tabular MDPs with aggregate bandit feedback. In the case of known transitions, our algorithms achieve $O(\log T)$ regret in stochastic settings and ${O}(\sqrt{T})$ regret in adversarial ones. Importantly, we also establish matching lower bounds, showing the optimality of our algorithms in this setting. We further extend our approach to unknown-transition settings by incorporating confidence-based techniques. Our results rely on a combination of FTRL over occupancy measures, self-bounding techniques, and new loss estimators inspired by recent advances in online shortest path problems. Along the way, we also provide the first individual-gap-dependent lower bounds and demonstrate near-optimal BOBW algorithms for shortest path problems with bandit feedback.

Theory · Reinforcement Learning and Planning

Aadirupa Saha, Robert Schapire

The problem of contextual dueling bandits is central to reinforcement learning with human feedback (RLHF), a widely used approach in AI alignment for incorporating human preferences into learning systems. Despite its importance, existing methods are constrained either by strong preference modeling assumptions or by applicability only to finite action spaces. Moreover, prior algorithms typically rely on online optimization oracles, which are computationally infeasible for complex function classes, limiting their practical effectiveness. In this work, we present the first fundamental theoretical study of general contextual dueling bandits over continuous action spaces. Our key contribution is a novel algorithm based on a regularized min-max optimization framework that achieves a regret bound of $\tilde{O}(\sqrt{dT})$—the first such guarantee for this general setting. By leveraging offline oracles instead of online ones, our method further improves computational efficiency. Empirical evaluations validate our theoretical findings, with our approach significantly outperforming existing baselines in terms of regret.

Theory · Reinforcement Learning and Planning

Amir Rezaei Balef, Claire Vernade, Katharina Eggensperger

The Combined Algorithm Selection and Hyperparameter optimization (CASH) is a challenging resource allocation problem in the field of AutoML. We propose MaxUCB, a max $k$-armed bandit method to trade off exploring different model classes and conducting hyperparameter optimization. MaxUCB is specifically designed for the light-tailed and bounded reward distributions arising in this setting and, thus, provides an efficient alternative compared to classic max $k$-armed bandit methods assuming heavy-tailed reward distributions. We theoretically and empirically evaluate our method on four standard AutoML benchmarks, demonstrating superior performance over prior approaches. We make our code and data available at https://github.com/amirbalef/CASH_with_Bandits

Theory · Reinforcement Learning and Planning

Hyun-jun Choi, Joongkyu Lee, Min-hwan Oh

We revisit the contextual cascading bandit, where a learning agent recommends an ordered list (\emph{cascade}) of items, and a user scans the list sequentially, stopping at the first attractive item. Although cascading bandits underpin various applications including recommender systems and search engines, the role of the cascade length $K$ in shaping regret has remained unclear. Contrary to prior results that regret grows with $K$, we prove that regret actually \emph{decreases} once $K$ is large enough. Leveraging this insight, we design a new upper-confidence-bound algorithm built on online mirror descent that attains the sharpest known regret upper bound, $\tilde{\mathcal{O}}\bigl(\min \lbrace K\bar{p}^{K-1}, 1 \rbrace d \sqrt{T}\bigr)$ for contextual cascading bandits. To complement this new regret upper bound, we provide a nearly matching lower bound of $\Omega \bigl(\min \lbrace K\underline{p}^{K-1}, 1 \rbrace d \sqrt{T}\bigr)$, where $0 \leq \underline{p} \leq \bar{p} < 1$. Together, these results fully characterize how regret truly scales with $K$, thereby closing the theoretical gap for contextual cascading bandits. Finally, comprehensive experiments validate our theoretical results and show the effectiveness of our proposed method.

Theory · Reinforcement Learning and Planning

Toshinori Kitamura, Arnob Ghosh, Tadashi Kozuno, Wataru Kumagai, Kazumi Kasaura, Kenta Hoshino, Yohei Hosoe, Yutaka Matsuo

We study the reinforcement learning (RL) problem in a constrained Markov decision process (CMDP), where an agent explores the environment to maximize the expected cumulative reward while satisfying a single constraint on the expected total utility value in every episode. While this problem is well understood in the tabular setting, theoretical results for function approximation remain scarce. This paper closes the gap by proposing an RL algorithm for linear CMDPs that achieves $\widetilde{\mathcal{O}}(\sqrt{K})$ regret with an episode-wise zero-violation guarantee. Furthermore, our method is computationally efficient, scaling polynomially with problem-dependent parameters while remaining independent of the state space size. Our results significantly improve upon recent linear CMDP algorithms, which either violate the constraint or incur exponential computational costs.

Theory · Reinforcement Learning and Planning

Yichen Li, Chicheng Zhang

Imitation learning (IL) is a paradigm for learning sequential decision-making policies from experts, leveraging offline demonstrations, interactive annotations, or both. Recent advances show that when annotation cost is tallied per trajectory, Behavior Cloning (BC)—which relies solely on offline demonstrations—cannot be improved in general, leaving limited conditions for interactive methods such as DAgger to help. We revisit this conclusion and prove that when the annotation cost is measured per state, algorithms using interactive annotations can provably outperform BC. Specifically: (1) we show that Stagger, a one‑sample‑per‑round variant of DAgger, provably beats BC under low-recovery-cost settings; (2) we initiate the study of hybrid IL where the agent learns from offline demonstrations and interactive annotations. We propose Warm-Stagger whose learning guarantee is not much worse than using either data source alone. Furthermore, motivated by compounding error and cold‑start problem in imitation learning practice, we give an MDP example in which Warm-Stagger has significant better annotation cost; (3) experiments on MuJoCo continuous‑control tasks confirm that, with modest cost ratio between interactive and offline annotations, interactive and hybrid approaches consistently outperform BC. To the best of our knowledge, our work is the first to highlight the benefit of state‑wise interactive annotation and hybrid feedback in imitation learning.

Theory · Reinforcement Learning and Planning

Shulun Chen, Runlong Zhou, Zihan Zhang, Maryam Fazel, Simon Du

We consider gap-dependent regret bounds for episodic MDPs. We show that the Monotonic Value Propagation (MVP) algorithm (Zhang et al. [2024]) achieves a variance-aware gap-dependent regret bound of $$\tilde{O}\left(\left(\sum_{\Delta_h(s,a)>0} \frac{H^2 \log K \land \mathtt{Var}\_{\max}^{\textup{c}}}{\Delta_h(s,a)} +\sum_{\Delta_h(s,a)=0}\frac{ H^2 \land \mathtt{Var}\_{\max}^{\textup{c}}}{\Delta_{\mathrm{min}}} + SAH^4 (S \lor H) \right) \log K\right),$$ where $H$ is the planning horizon, $S$ is the number of states, $A$ is the number of actions, $K$ is the number of episodes, and $\tilde{O}$ hides $\mathsf{poly} \log (S, A, H, 1 / \Delta\_{\mathrm{min}}, 1 / \delta)$ terms. Here, $\Delta_h(s,a) =V_h^* (a) - Q_h^* (s, a)$ represents the suboptimality gap and $\Delta_{\mathrm{min}} := \min_{\Delta_h (s,a) > 0} \Delta_h(s,a)$. The term $\mathtt{Var}\_{\max}^{\textup{c}}$ denotes the maximum conditional total variance, calculated as the maximum over all $(\pi, h, s)$ tuples of the expected total variance under policy $\pi$ conditioned on trajectories visiting state $s$ at step $h$. $\mathtt{Var}\_{\max}^{\textup{c}}$ characterizes the maximum randomness encountered when learning any $(h, s)$ pair. Our result stems from a novel analysis of the weighted sum of the suboptimality gap and can be potentially adapted for other algorithms. To complement the study, we establish a lower bound of $$\Omega \left( \sum_{\Delta_h(s,a)>0} \frac{H^2 \land \mathtt{Var}\_{\max}^{\textup{c}}}{\Delta_h(s,a)}\cdot \log K\right),$$ demonstrating the necessity of dependence on $\mathtt{Var}\_{\max}^{\textup{c}}$ even when the maximum unconditional total variance (without conditioning on $(h, s)$) approaches zero.

Reinforcement Learning · Deep RL

Donghyeon Ki, JunHyeok Oh, Seong-Woong Shim, Byung-Jun Lee

Diffusion models have recently gained prominence in offline reinforcement learning due to their ability to effectively learn high-performing, generalizable policies from static datasets. Diffusion-based planners facilitate long-horizon decision-making by generating high-quality trajectories through iterative denoising, guided by return-maximizing objectives. However, existing guided sampling strategies such as Classifier Guidance, Classifier-Free Guidance, and Monte Carlo Sample Selection either produce suboptimal multi-modal actions, struggle with distributional drift, or incur prohibitive inference-time costs. To address these challenges, we propose \textbf{\textit{Prior Guidance}} (PG), a novel guided sampling framework that replaces the standard Gaussian prior of a behavior-cloned diffusion model with a learnable distribution, optimized via a behavior-regularized objective. PG directly generates high-value trajectories without costly reward optimization of the diffusion model itself, and eliminates the need to sample multiple candidates at inference for sample selection. We present an efficient training strategy that applies behavior regularization in latent space, and empirically demonstrate that PG outperforms state-of-the-art diffusion policies and planners across diverse long-horizon offline RL benchmarks. Our code is available at https://github.com/ku-dmlab/PG.

Theory · Reinforcement Learning and Planning

Liad Erez, Tomer Koren

We study the problem of contextual combinatorial semi-bandits, where input contexts are mapped into subsets of size $m$ of a collection of $K$ possible actions. In each round of the interaction, the learner observes feedback consisting of the realized reward of the predicted actions. Motivated by prototypical applications of contextual bandits, we focus on the $s$-sparse regime where we assume that the sum of rewards is bounded by some value $s \ll K$. For example, in recommendation systems the number of products purchased by any customer is significantly smaller than the total number of available products. Our main result is for the $(\varepsilon,\delta)$-PAC variant of the problem for which we design an algorithm that returns an $\varepsilon$-optimal policy with high probability using a sample complexity of $\widetilde{O}\big( (\mathrm{poly}(K/m) + sm / \varepsilon^2) \log (|\Pi|/\delta) \big)$ where $\Pi$ is the underlying (finite) class and $s$ is the sparsity parameter. This bound improves upon known bounds for combinatorial semi-bandits whenever $s \ll K$, and in the regime where $s = O(1)$, the leading terms in our bound match the corresponding full-information rates, implying that bandit feedback essentially comes at no cost. Our PAC learning algorithm is also computationally efficient given access to an ERM oracle for $\Pi$. Our framework generalizes the list multiclass classification problem with bandit feedback, which can be seen as a special case with binary reward vectors. In the special case of single-label classification corresponding to $s=m=1$, we prove an $O \big((K^7 + 1/\varepsilon^2)\log (|\mathcal{H}|/\delta)\big)$ sample complexity bound for a finite hypothesis class $\mathcal{H}$, which improves upon recent results in this scenario. Additionally, we consider the regret minimization setting where data can be generated adversarially, and establish a regret bound of $\widetilde O(|\Pi| + \sqrt{smT \log |\Pi|})$, extending the result of Erez et al. ('24) who consider the simpler single label classification setting.

Theory · Reinforcement Learning and Planning

Zixuan Xie, Xinyu Liu, Rohan Chandra, Shangtong Zhang

Linear TD($\lambda$) is one of the most fundamental reinforcement learning algorithms for policy evaluation. Previously, convergence rates are typically established under the assumption of linearly independent features, which does not hold in many practical scenarios. This paper instead establishes the first $L^2$ convergence rates for linear TD($\lambda$) operating under arbitrary features, without making any algorithmic modification or additional assumptions. Our results apply to both the discounted and average-reward settings. To address the potential non-uniqueness of solutions resulting from arbitrary features, we develop a novel stochastic approximation result featuring convergence rates to the solution set instead of a single point.

Theory · Reinforcement Learning and Planning

Kehan Long, Jorge Cortes, Nikolay Atanasov

Establishing stability certificates for closed-loop systems under reinforcement learning (RL) policies is essential to move beyond empirical performance and offer guarantees of system behavior. Classical Lyapunov methods require a strict stepwise decrease in the Lyapunov function but such certificates are difficult to construct for learned policies. The RL value function is a natural candidate but it is not well understood how it can be adapted for this purpose. To gain intuition, we first study the linear quadratic regulator (LQR) problem and make two key observations. First, a Lyapunov function can be obtained from the value function of an LQR policy by augmenting it with a residual term related to the system dynamics and stage cost. Second, the classical Lyapunov decrease requirement can be relaxed to a generalized Lyapunov condition requiring only decrease on average over multiple time steps. Using this intuition, we consider the nonlinear setting and formulate an approach to learn generalized Lyapunov functions by augmenting RL value functions with neural network residual terms. Our approach successfully certifies the stability of RL policies trained on Gymnasium and DeepMind Control benchmarks. We also extend our method to jointly train neural controllers and stability certificates using a multi-step Lyapunov loss, resulting in larger certified inner approximations of the region of attraction compared to the classical Lyapunov approach. Overall, our formulation enables stability certification for a broad class of systems with learned policies by making certificates easier to construct, thereby bridging classical control theory and modern learning-based methods.

Theory · Reinforcement Learning and Planning

Ruijia Liu, Ancheng Hou, Xiao Yu, Xiang Yin

Signal Temporal Logic (STL) is a powerful specification language for describing complex temporal behaviors of continuous signals, making it well-suited for high-level robotic task descriptions. However, generating executable plans for STL tasks is challenging, as it requires consideration of the coupling between the task specification and the system dynamics. Existing approaches either follow a model-based setting that explicitly requires knowledge of the system dynamics or adopt a task-oriented data-driven approach to learn plans for specific tasks. In this work, we address the problem of generating executable STL plans for systems with unknown dynamics. We propose a hierarchical planning framework that enables zero-shot generalization to new STL tasks by leveraging only task-agnostic trajectory data during offline training. The framework consists of three key components: (i) decomposing the STL specification into several progresses and time constraints, (ii) searching for timed waypoints that satisfy all progresses under time constraints, and (iii) generating trajectory segments using a pre-trained diffusion model and stitching them into complete trajectories. We formally prove that our method guarantees STL satisfaction, and simulation results demonstrate its effectiveness in generating dynamically feasible trajectories across diverse long-horizon STL tasks. Project Page: https://cps-sjtu.github.io/Zero-Shot-STL/

Theory · Reinforcement Learning and Planning

Alireza Bakhtiari, Alex Ayoub, Samuel Robertson, David Janz, Csaba Szepesvari

We establish a lower bound on the eluder dimension in generalised linear model classes, showing that standard eluder dimension-based analysis cannot lead to first-order regret bounds. To address this, we introduce a localisation method for the eluder dimension; our analysis immediately recovers and improves on classic results for Bernoulli bandits, and allows for the first genuine first-order bounds for finite-horizon reinforcement learning tasks with bounded cumulative returns.