Finite-Sample Analysis of the Monte Carlo Exploring Starts Algorithm for Reinforcement Learning

• URL: http://arxiv.org/abs/2410.02994v1
• Date: Thu, 3 Oct 2024 21:11:29 GMT
• Title: Finite-Sample Analysis of the Monte Carlo Exploring Starts Algorithm for Reinforcement Learning
• Authors: Suei-Wen Chen, Keith Ross, Pierre Youssef,
• Abstract summary: We prove a novel result on the convergence rate of the policy algorithm. We show that the algorithm returns an optimal policy after $tildeO(SAK3log3frac1delta)$ sampled episodes.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Monte Carlo Exploring Starts (MCES), which aims to learn the optimal policy using only sample returns, is a simple and natural algorithm in reinforcement learning which has been shown to converge under various conditions. However, the convergence rate analysis for MCES-style algorithms in the form of sample complexity has received very little attention. In this paper we develop a finite sample bound for a modified MCES algorithm which solves the stochastic shortest path problem. To this end, we prove a novel result on the convergence rate of the policy iteration algorithm. This result implies that with probability at least $1-\delta$, the algorithm returns an optimal policy after $\tilde{O}(SAK^3\log^3\frac{1}{\delta})$ sampled episodes, where $S$ and $A$ denote the number of states and actions respectively, $K$ is a proxy for episode length, and $\tilde{O}$ hides logarithmic factors and constants depending on the rewards of the environment that are assumed to be known.

Related papers

• Provable Policy Gradient Methods for Average-Reward Markov Potential Games [15.136494705127564]
  We study Markov potential games under the infinite horizon average reward criterion. We prove that both algorithms based on independent policy gradient and independent natural policy gradient converge globally to a Nash equilibrium for the average reward criterion.
  arXiv  Detail & Related papers  (2024-03-09T00:20:33Z)
• A Doubly Robust Approach to Sparse Reinforcement Learning [19.68978899041642]
  We propose a new regret algorithm for episodic sparse linear Markov decision process (SMDP) The proposed algorithm is $tildeO(sigma-1_min s_star H sqrtN)$, where $sigma_min$ denotes the restrictive minimum eigenvalue of the average Gram matrix of feature vectors.
  arXiv  Detail & Related papers  (2023-10-23T18:52:17Z)
• Efficiently Learning One-Hidden-Layer ReLU Networks via Schur Polynomials [50.90125395570797]
  We study the problem of PAC learning a linear combination of $k$ ReLU activations under the standard Gaussian distribution on $mathbbRd$ with respect to the square loss. Our main result is an efficient algorithm for this learning task with sample and computational complexity $(dk/epsilon)O(k)$, whereepsilon>0$ is the target accuracy.
  arXiv  Detail & Related papers  (2023-07-24T14:37:22Z)
• Reaching Goals is Hard: Settling the Sample Complexity of the Stochastic Shortest Path [106.37656068276902]
  We study the sample complexity of learning an $epsilon$-optimal policy in the Shortest Path (SSP) problem. We derive complexity bounds when the learner has access to a generative model. We show that there exists a worst-case SSP instance with $S$ states, $A$ actions, minimum cost $c_min$, and maximum expected cost of the optimal policy over all states $B_star$.
  arXiv  Detail & Related papers  (2022-10-10T18:34:32Z)
• Best Policy Identification in Linear MDPs [70.57916977441262]
  We investigate the problem of best identification in discounted linear Markov+Delta Decision in the fixed confidence setting under a generative model. The lower bound as the solution of an intricate non- optimization program can be used as the starting point to devise such algorithms.
  arXiv  Detail & Related papers  (2022-08-11T04:12:50Z)
• Randomized Exploration for Reinforcement Learning with General Value Function Approximation [122.70803181751135]
  We propose a model-free reinforcement learning algorithm inspired by the popular randomized least squares value iteration (RLSVI) algorithm. Our algorithm drives exploration by simply perturbing the training data with judiciously chosen i.i.d. scalar noises. We complement the theory with an empirical evaluation across known difficult exploration tasks.
  arXiv  Detail & Related papers  (2021-06-15T02:23:07Z)
• Improved Sample Complexity for Incremental Autonomous Exploration in MDPs [132.88757893161699]
  We learn the set of $epsilon$-optimal goal-conditioned policies attaining all states that are incrementally reachable within $L$ steps. DisCo is the first algorithm that can return an $epsilon/c_min$-optimal policy for any cost-sensitive shortest-path problem.
  arXiv  Detail & Related papers  (2020-12-29T14:06:09Z)
• On the Convergence of Reinforcement Learning with Monte Carlo Exploring Starts [5.137144629366217]
  A basic simulation-based reinforcement learning algorithm is the Monte Carlo Exploring States (MCES) method. We investigate the convergence of this algorithm for the case with undiscounted costs, also known as the shortest path problem. As a side result, we also provide a proof of a version of the supermartingale convergence theorem commonly used in approximation.
  arXiv  Detail & Related papers  (2020-07-21T16:19:09Z)
• Model-Free Reinforcement Learning: from Clipped Pseudo-Regret to Sample Complexity [59.34067736545355]
  Given an MDP with $S$ states, $A$ actions, the discount factor $gamma in (0,1)$, and an approximation threshold $epsilon > 0$, we provide a model-free algorithm to learn an $epsilon$-optimal policy. For small enough $epsilon$, we show an improved algorithm with sample complexity.
  arXiv  Detail & Related papers  (2020-06-06T13:34:41Z)

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.