Landscape of Policy Optimization for Finite Horizon MDPs with General State and Action

• URL: http://arxiv.org/abs/2409.17138v1
• Date: Wed, 25 Sep 2024 17:56:02 GMT
• Title: Landscape of Policy Optimization for Finite Horizon MDPs with General State and Action
• Authors: Xin Chen, Yifan Hu, Minda Zhao,
• Abstract summary: We develop a framework for a class of Markov Decision Processes with general state and spaces. We show that gradient methods converge to the globally optimal policy with a nonasymptomatic condition. Our result establishes first complexity for multi-period inventory systems.
• Score: 10.219627570276689
• License: http://creativecommons.org/licenses/by-nc-sa/4.0/
• Abstract: Policy gradient methods are widely used in reinforcement learning. Yet, the nonconvexity of policy optimization imposes significant challenges in understanding the global convergence of policy gradient methods. For a class of finite-horizon Markov Decision Processes (MDPs) with general state and action spaces, we develop a framework that provides a set of easily verifiable assumptions to ensure the Kurdyka-Lojasiewicz (KL) condition of the policy optimization. Leveraging the KL condition, policy gradient methods converge to the globally optimal policy with a non-asymptomatic rate despite nonconvexity. Our results find applications in various control and operations models, including entropy-regularized tabular MDPs, Linear Quadratic Regulator (LQR) problems, stochastic inventory models, and stochastic cash balance problems, for which we show an $\epsilon$-optimal policy can be obtained using a sample size in $\tilde{\mathcal{O}}(\epsilon^{-1})$ and polynomial in terms of the planning horizon by stochastic policy gradient methods. Our result establishes the first sample complexity for multi-period inventory systems with Markov-modulated demands and stochastic cash balance problems in the literature.

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