Thompson sampling for linear quadratic mean-field teams

11/09/2020

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by   Mukul Gagrani, et al.

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We consider optimal control of an unknown multi-agent linear quadratic (LQ) system where the dynamics and the cost are coupled across the agents through the mean-field (i.e., empirical mean) of the states and controls. Directly using single-agent LQ learning algorithms in such models results in regret which increases polynomially with the number of agents. We propose a new Thompson sampling based learning algorithm which exploits the structure of the system model and show that the expected Bayesian regret of our proposed algorithm for a system with agents of |M| different types at time horizon T is 𝒪̃( |M|^1.5√(T)) irrespective of the total number of agents, where the 𝒪̃ notation hides logarithmic factors in T. We present detailed numerical experiments to illustrate the salient features of the proposed algorithm.