Linear-Quadratic Mean-Field Reinforcement Learning: Convergence of Policy Gradient Methods

René Carmona; Mathieu Laurière; Zongjun Tan

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arXiv · 1910.04295

Linear-Quadratic Mean-Field Reinforcement Learning: Convergence of Policy Gradient Methods

René Carmona·Mathieu Laurière·Zongjun Tan

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Abstract

We investigate reinforcement learning in the setting of Markov decision processes for a large number of exchangeable agents interacting in a mean field manner. Applications include, for example, the control of a large number of robots communicating through a central unit dispatching the optimal policy computed by maximizing an aggregate reward. An approximate solution is obtained by learning the optimal policy of a generic agent interacting with the statistical distribution of the states and actions of the other agents. We first provide a full analysis this discrete-time mean field control problem. We then rigorously prove the convergence of exact and model-free policy gradient methods in a mean-field linear-quadratic setting and establish bounds on the rates of convergence. We also provide graphical evidence of the convergence based on implementations of our algorithms.

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BibTeX RIS

René Carmona, Mathieu Laurière, Zongjun Tan. 2019-10-09. Linear-Quadratic Mean-Field Reinforcement Learning: Convergence of Policy Gradient Methods. https://arxiv.org/abs/1910.04295

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