On the Sample Complexity of Discounted Reinforcement Learning with Optimized Certainty Equivalents

• URL: http://arxiv.org/abs/2605.21763v1
• Date: Wed, 20 May 2026 21:53:51 GMT
• Title: On the Sample Complexity of Discounted Reinforcement Learning with Optimized Certainty Equivalents
• Abstract summary: We study risk-sensitive reinforcement learning in finite discounted MDPs.<n>We consider a family or risk measures called the optimized certainty equivalent (OCE)
• Score: 2.4145441422386464
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We study risk-sensitive reinforcement learning in finite discounted MDPs, where a generative model of the MDP is assumed to be available. We consider a family or risk measures called the optimized certainty equivalent (OCE), which includes important risk measures such as entropic risk, CVaR, and mean-variance. Our focus is on the sample complexities of learning the optimal state-action value function (value learning) and an optimal policy (policy learning) under recursive OCE. We provide an exact characterization of utility functions $u$ for which the corresponding OCE defines an objective that is PAC-learnable. We analyze a simple model-based approach and derive PAC sample complexity bounds. We establish that whenever $u$ does not have full domain $\text{dom}(u)\neq \mathbb{R}$, the corresponding problem is not PAC-learnable. Finally, we establish corresponding lower bounds for both value and policy learning, demonstrating tightness in the size $SA$ of state-action space, and for a more restricted class of utilities, we derive lower bounds that makes the dependence on the effective horizon $\frac{1}{1-γ}$ explicit. Specifically, for $\text{CVaR}_τ$ we show that the correct dependence on $τ$ is $\frac{1}{τ^2}$, thus improving by a factor of $\frac{1}τ$ over state-of-the-art although our bound has a suboptimal dependence on $\frac{1}{1-γ}$.

Related papers

• Wasserstein Policy Learning for Distributional Outcomes [19.98190660365478]
  We study offline policy learning with distribution-valued outcomes.<n>We establish statistical guarantees for the policy learning framework.<n>We provide a minimax lower bound establishing the sharpness of the leading dependence on $N and $mathrmNtext-dim()/N.
  arXiv  Detail & Related papers  (2026-06-17T14:31:53Z)
• Provably Efficient Sample Complexity for Robust CMDP [7.060086147428817]
  We study the problem of learning policies that maximize cumulative reward while satisfying safety constraints.<n>We focus on robust constrained Markov decision processes (RCMDPs), where the agent must maximize reward while ensuring cumulative utility exceeds a threshold.<n>We propose a novel Robust constrained Value iteration (RCVI) algorithm with a sample complexity of $mathcaltildeO(|S||A|H5/2)$ achieving at most $$ violations.
  arXiv  Detail & Related papers  (2025-11-10T04:40:37Z)
• Near-Optimal Sample Complexity Bounds for Constrained Average-Reward MDPs [6.237808815887583]
  We study the sample complexity of learning an $epsilon$-optimal policy in constrained average-reward MDPs under a generative model.<n>Our results close the theoretical gap in understanding the complexity of constrained average-reward MDPs.
  arXiv  Detail & Related papers  (2025-09-20T09:19:42Z)
• Convergence and Sample Complexity of First-Order Methods for Agnostic Reinforcement Learning [66.4260157478436]
  We study reinforcement learning in the policy learning setting.<n>The goal is to find a policy whose performance is competitive with the best policy in a given class of interest.
  arXiv  Detail & Related papers  (2025-07-06T14:40:05Z)
• Provably Sample-Efficient Robust Reinforcement Learning with Average Reward [4.530028899565083]
  We propose a new algorithm designed for robust Markov Decision Processes (MDPs) with transition uncertainty characterized by $ell_p$-norm and contamination models.<n>Our algorithm operates without requiring any prior knowledge of the robust MDP.<n>Our work provides essential theoretical understanding of sample efficiency of robust average reward RL.
  arXiv  Detail & Related papers  (2025-05-18T15:34:45Z)
• Towards a Sharp Analysis of Offline Policy Learning for $f$-Divergence-Regularized Contextual Bandits [49.96531901205305]
  We analyze $f$-divergence-regularized offline policy learning.<n>For reverse Kullback-Leibler (KL) divergence, we give the first $tildeO(epsilon-1)$ sample complexity under single-policy concentrability.<n>We extend our analysis to dueling bandits, and we believe these results take a significant step toward a comprehensive understanding of $f$-divergence-regularized policy learning.
  arXiv  Detail & Related papers  (2025-02-09T22:14:45Z)
• A Finite-Sample Analysis of an Actor-Critic Algorithm for Mean-Variance Optimization in a Discounted MDP [1.0923877073891446]
  We analyze a Temporal Difference (TD) learning algorithm with linear function approximation (LFA) for policy evaluation.<n>We derive finite-sample bounds that hold (i) in the mean-squared sense and (ii) with high probability under tail iterate averaging.<n>These results establish finite-sample theoretical guarantees for risk-sensitive actor-critic methods in reinforcement learning.
  arXiv  Detail & Related papers  (2024-06-12T05:49:53Z)
• Sample-Efficient Constrained Reinforcement Learning with General Parameterization [35.22742439337603]
  We consider a constrained Markov Decision Problem (CMDP) where the goal of an agent is to maximize the expected discounted sum of rewards over an infinite horizon. We develop the Primal-Dual Accelerated Natural Policy Gradient (PD-ANPG) algorithm that ensures an $epsilon$ global optimality gap and $epsilon$ constraint violation.
  arXiv  Detail & Related papers  (2024-05-17T08:39:05Z)
• Scalable Online Exploration via Coverability [45.66375686120087]
  Exploration is a major challenge in reinforcement learning, especially for high-dimensional domains that require function approximation. We introduce a new objective, $L_Coverage, which generalizes previous exploration schemes and supports three fundamental desideratas. $L_Coverage enables the first computationally efficient model-based and model-free algorithms for online (reward-free or reward-driven) reinforcement learning in MDPs with low coverability.
  arXiv  Detail & Related papers  (2024-03-11T10:14:06Z)
• A Nearly Optimal and Low-Switching Algorithm for Reinforcement Learning with General Function Approximation [67.66904892192794]
  We propose a new algorithm, Monotonic Q-Learning with Upper Confidence Bound (MQL-UCB) for reinforcement learning.<n>MQL-UCB achieves minimax optimal regret of $tildeO(dsqrtHK)$ when $K$ is sufficiently large and near-optimal policy switching cost.<n>Our work sheds light on designing provably sample-efficient and deployment-efficient Q-learning with nonlinear function approximation.
  arXiv  Detail & Related papers  (2023-11-26T08:31:57Z)
• Provably Efficient CVaR RL in Low-rank MDPs [58.58570425202862]
  We study risk-sensitive Reinforcement Learning (RL) We propose a novel Upper Confidence Bound (UCB) bonus-driven algorithm to balance interplay between exploration, exploitation, and representation learning in CVaR RL. We prove that our algorithm achieves a sample complexity of $epsilon$-optimal CVaR, where $H$ is the length of each episode, $A$ is the capacity of action space, and $d$ is the dimension of representations.
  arXiv  Detail & Related papers  (2023-11-20T17:44:40Z)
• Improved Regret for Efficient Online Reinforcement Learning with Linear Function Approximation [69.0695698566235]
  We study reinforcement learning with linear function approximation and adversarially changing cost functions. We present a computationally efficient policy optimization algorithm for the challenging general setting of unknown dynamics and bandit feedback.
  arXiv  Detail & Related papers  (2023-01-30T17:26:39Z)
• Near-Optimal Deployment Efficiency in Reward-Free Reinforcement Learning with Linear Function Approximation [16.871660060209674]
  We study the problem of deployment efficient reinforcement learning (RL) with linear function approximation under the emphreward-free exploration setting. We propose a new algorithm that collects at most $widetildeO(fracd2H5epsilon2)$ trajectories within $H$ deployments to identify $epsilon$-optimal policy for any (possibly data-dependent) choice of reward functions.
  arXiv  Detail & Related papers  (2022-10-03T03:48:26Z)
• Nearly Optimal Latent State Decoding in Block MDPs [74.51224067640717]
  In episodic Block MDPs, the decision maker has access to rich observations or contexts generated from a small number of latent states. We are first interested in estimating the latent state decoding function based on data generated under a fixed behavior policy. We then study the problem of learning near-optimal policies in the reward-free framework.
  arXiv  Detail & Related papers  (2022-08-17T18:49:53Z)
• Provably Efficient Safe Exploration via Primal-Dual Policy Optimization [105.7510838453122]
  We study the Safe Reinforcement Learning (SRL) problem using the Constrained Markov Decision Process (CMDP) formulation. We present an provably efficient online policy optimization algorithm for CMDP with safe exploration in the function approximation setting.
  arXiv  Detail & Related papers  (2020-03-01T17:47:03Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.