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We study the policy evaluation problem in multi-agent reinforcement learning.In this problem, a group of agents works cooperatively to evaluate the valuefunction for the global discounted accumulative reward problem, which iscomposed of local rewards observed by the agents. Over a series of time steps,the agents act, get rewarded, update their local estimate of the valuefunction, then communicate with their neighbors. The local update at each agentcan be interpreted as a distributed consensus-based variant of the populartemporal difference learning algorithm TD(0).  While distributed reinforcement learning algorithms have been presented inthe literature, almost nothing is known about their convergence rate. Our maincontribution is providing a finite-time analysis for the convergence of thedistributed TD(0) algorithm. We do this when the communication network betweenthe agents is time-varying in general. We obtain an explicit upper bound on therate of convergence of this algorithm as a function of the network topology andthe discount factor. Our results mirror what we would expect from usingdistributed stochastic gradient descent for solving convex optimizationproblems.

Finite-Time Analysis of Distributed TD(0) with Linear Function Approximation for Multi-Agent Reinforcement Learning