Game-theoretical control with continuous action sets

Perkins, Steven and Mertikopoulos, Panayotis and Leslie, David S. (2014) Game-theoretical control with continuous action sets. Working Paper. UNSPECIFIED. (Unpublished)

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Motivated by the recent applications of game-theoretical learning techniques to the design of distributed control systems, we study a class of control problems that can be formulated as potential games with continuous action sets, and we propose an actor-critic reinforcement learning algorithm that provably converges to equilibrium in this class of problems. The method employed is to analyse the learning process under study through a mean-field dynamical system that evolves in an infinite-dimensional function space (the space of probability distributions over the players' continuous controls). To do so, we extend the theory of finite-dimensional two-timescale stochastic approximation to an infinite-dimensional, Banach space setting, and we prove that the continuous dynamics of the process converge to equilibrium in the case of potential games. These results combine to give a provably-convergent learning algorithm in which players do not need to keep track of the controls selected by the other agents.

Item Type:
Monograph (Working Paper)
Uncontrolled Keywords:
math.OC ; cs.GT ; cs.MA ; stat.ML
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Deposited On:
04 Dec 2014 09:43
Last Modified:
11 Jun 2019 01:48