FiniteTime Analysis of Distributed TD(0) with Linear Function Approximation on MultiAgent Reinforcement Learning
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Proceedings of the 36th International Conference on Machine Learning, PMLR 97:16261635, 2019.
Abstract
We study the policy evaluation problem in multiagent reinforcement learning. In this problem, a group of agents works cooperatively to evaluate the value function for the global discounted accumulative reward problem, which is composed of local rewards observed by the agents. Over a series of time steps, the agents act, get rewarded, update their local estimate of the value function, then communicate with their neighbors. The local update at each agent can be interpreted as a distributed consensusbased variant of the popular temporal difference learning algorithm TD(0). While distributed reinforcement learning algorithms have been presented in the literature, almost nothing is known about their convergence rate. Our main contribution is providing a finitetime analysis for the convergence of the distributed TD(0) algorithm. We do this when the communication network between the agents is timevarying in general. We obtain an explicit upper bound on the rate of convergence of this algorithm as a function of the network topology and the discount factor. Our results mirror what we would expect from using distributed stochastic gradient descent for solving convex optimization problems.
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