A Finite-Sample Analysis of an Actor-Critic Algorithm for Mean-Variance Optimization in a Discounted MDP

• URL: http://arxiv.org/abs/2406.07892v2
• Date: Wed, 12 Mar 2025 14:32:31 GMT
• Title: A Finite-Sample Analysis of an Actor-Critic Algorithm for Mean-Variance Optimization in a Discounted MDP
• Authors: Tejaram Sangadi, L. A. Prashanth, Krishna Jagannathan,
• Abstract summary: 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.
• Score: 1.0923877073891446
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Motivated by applications in risk-sensitive reinforcement learning, we study mean-variance optimization in a discounted reward Markov Decision Process (MDP). Specifically, we analyze a Temporal Difference (TD) learning algorithm with linear function approximation (LFA) for policy evaluation. We derive finite-sample bounds that hold (i) in the mean-squared sense and (ii) with high probability under tail iterate averaging, both with and without regularization. Our bounds exhibit an exponentially decaying dependence on the initial error and a convergence rate of $O(1/t)$ after $t$ iterations. Moreover, for the regularized TD variant, our bound holds for a universal step size. Next, we integrate a Simultaneous Perturbation Stochastic Approximation (SPSA)-based actor update with an LFA critic and establish an $O(n^{-1/4})$ convergence guarantee, where $n$ denotes the iterations of the SPSA-based actor-critic algorithm. These results establish finite-sample theoretical guarantees for risk-sensitive actor-critic methods in reinforcement learning, with a focus on variance as a risk measure.

Related papers

• Model-Based Epistemic Variance of Values for Risk-Aware Policy Optimization [59.758009422067]
  We consider the problem of quantifying uncertainty over expected cumulative rewards in model-based reinforcement learning. We propose a new uncertainty Bellman equation (UBE) whose solution converges to the true posterior variance over values. We introduce a general-purpose policy optimization algorithm, Q-Uncertainty Soft Actor-Critic (QU-SAC) that can be applied for either risk-seeking or risk-averse policy optimization.
  arXiv  Detail & Related papers  (2023-12-07T15:55:58Z)
• Improved High-Probability Bounds for the Temporal Difference Learning Algorithm via Exponential Stability [17.771354881467435]
  We show that a simple algorithm with a universal and instance-independent step size is sufficient to obtain near-optimal variance and bias terms. Our proof technique is based on refined error bounds for linear approximation together with the novel stability result for the product of random matrices.
  arXiv  Detail & Related papers  (2023-10-22T12:37:25Z)
• Variance-Dependent Regret Bounds for Linear Bandits and Reinforcement Learning: Adaptivity and Computational Efficiency [90.40062452292091]
  We present the first computationally efficient algorithm for linear bandits with heteroscedastic noise. Our algorithm is adaptive to the unknown variance of noise and achieves an $tildeO(d sqrtsum_k = 1K sigma_k2 + d)$ regret. We also propose a variance-adaptive algorithm for linear mixture Markov decision processes (MDPs) in reinforcement learning.
  arXiv  Detail & Related papers  (2023-02-21T00:17:24Z)
• Sharp Variance-Dependent Bounds in Reinforcement Learning: Best of Both Worlds in Stochastic and Deterministic Environments [48.96971760679639]
  We study variance-dependent regret bounds for Markov decision processes (MDPs) We propose two new environment norms to characterize the fine-grained variance properties of the environment. For model-based methods, we design a variant of the MVP algorithm. In particular, this bound is simultaneously minimax optimal for both and deterministic MDPs.
  arXiv  Detail & Related papers  (2023-01-31T06:54:06Z)
• Finite time analysis of temporal difference learning with linear function approximation: Tail averaging and regularisation [44.27439128304058]
  We study the finite-time behaviour of the popular temporal difference (TD) learning algorithm when combined with tail-averaging. We derive finite time bounds on the parameter error of the tail-averaged TD iterate under a step-size choice.
  arXiv  Detail & Related papers  (2022-10-12T04:37:54Z)
• Maximum-Likelihood Inverse Reinforcement Learning with Finite-Time Guarantees [56.848265937921354]
  Inverse reinforcement learning (IRL) aims to recover the reward function and the associated optimal policy. Many algorithms for IRL have an inherently nested structure. We develop a novel single-loop algorithm for IRL that does not compromise reward estimation accuracy.
  arXiv  Detail & Related papers  (2022-10-04T17:13:45Z)
• Momentum Accelerates the Convergence of Stochastic AUPRC Maximization [80.8226518642952]
  We study optimization of areas under precision-recall curves (AUPRC), which is widely used for imbalanced tasks. We develop novel momentum methods with a better iteration of $O (1/epsilon4)$ for finding an $epsilon$stationary solution. We also design a novel family of adaptive methods with the same complexity of $O (1/epsilon4)$, which enjoy faster convergence in practice.
  arXiv  Detail & Related papers  (2021-07-02T16:21:52Z)
• Parallel Stochastic Mirror Descent for MDPs [72.75921150912556]
  We consider the problem of learning the optimal policy for infinite-horizon Markov decision processes (MDPs) Some variant of Mirror Descent is proposed for convex programming problems with Lipschitz-continuous functionals. We analyze this algorithm in a general case and obtain an estimate of the convergence rate that does not accumulate errors during the operation of the method.
  arXiv  Detail & Related papers  (2021-02-27T19:28:39Z)
• Finite-Sample Analysis of Off-Policy Natural Actor-Critic Algorithm [4.932130498861987]
  We provide finite-sample convergence guarantees for an off-policy variant of the natural actor-critic (NAC) algorithm based on Importance Sampling. We show that the algorithm converges to a global optimal policy with a sample complexity of $mathcalO(epsilon-3log2(1/epsilon)$ under an appropriate choice of stepsizes.
  arXiv  Detail & Related papers  (2021-02-18T13:22:59Z)
• Variance Penalized On-Policy and Off-Policy Actor-Critic [60.06593931848165]
  We propose on-policy and off-policy actor-critic algorithms that optimize a performance criterion involving both mean and variance in the return. Our approach not only performs on par with actor-critic and prior variance-penalization baselines in terms of expected return, but also generates trajectories which have lower variance in the return.
  arXiv  Detail & Related papers  (2021-02-03T10:06:16Z)
• A Lyapunov Theory for Finite-Sample Guarantees of Asynchronous Q-Learning and TD-Learning Variants [39.28675942566465]
  This paper develops a framework to study finite-sample convergence guarantees of a class of value-based asynchronous RL algorithms. As a by-product, we provide theoretical insights into the bias-variance trade-off, i.e., efficiency of bootstrapping in RL.
  arXiv  Detail & Related papers  (2021-02-02T15:48:19Z)
• Simple and optimal methods for stochastic variational inequalities, II: Markovian noise and policy evaluation in reinforcement learning [9.359939442911127]
  This paper focuses on resetting variational inequalities (VI) under Markovian noise. A prominent application of our algorithmic developments is the policy evaluation problem in reinforcement learning.
  arXiv  Detail & Related papers  (2020-11-15T04:05:22Z)
• Variance-Reduced Off-Policy TDC Learning: Non-Asymptotic Convergence Analysis [27.679514676804057]
  We develop a variance reduction scheme for the two time-scale TDC algorithm in the off-policy setting. Experiments demonstrate that the proposed variance-reduced TDC achieves a smaller convergence error than both the conventional TDC and the variance-reduced TD.
  arXiv  Detail & Related papers  (2020-10-26T01:33:05Z)
• Private Stochastic Non-Convex Optimization: Adaptive Algorithms and Tighter Generalization Bounds [72.63031036770425]
  We propose differentially private (DP) algorithms for bound non-dimensional optimization. We demonstrate two popular deep learning methods on the empirical advantages over standard gradient methods.
  arXiv  Detail & Related papers  (2020-06-24T06:01:24Z)
• Is Temporal Difference Learning Optimal? An Instance-Dependent Analysis [102.29671176698373]
  We address the problem of policy evaluation in discounted decision processes, and provide Markov-dependent guarantees on the $ell_infty$error under a generative model. We establish both and non-asymptotic versions of local minimax lower bounds for policy evaluation, thereby providing an instance-dependent baseline by which to compare algorithms.
  arXiv  Detail & Related papers  (2020-03-16T17:15:28Z)
• Distributional Robustness and Regularization in Reinforcement Learning [62.23012916708608]
  We introduce a new regularizer for empirical value functions and show that it lower bounds the Wasserstein distributionally robust value function. It suggests using regularization as a practical tool for dealing with $textitexternal uncertainty$ in reinforcement learning.
  arXiv  Detail & Related papers  (2020-03-05T19:56:23Z)

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.