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

TL;DR

This paper provides the first finite-time convergence analysis of a distributed TD(0) algorithm with linear function approximation in multi-agent reinforcement learning, accounting for time-varying communication networks.

Contribution

It introduces a finite-time convergence bound for distributed TD(0) with linear function approximation in multi-agent settings, considering dynamic network topologies.

Findings

Explicit convergence rate bounds as a function of network topology and discount factor

Demonstrates that distributed TD(0) converges in finite time under certain conditions

Aligns the convergence behavior with that of distributed stochastic gradient descent

Abstract

We study the policy evaluation problem in multi-agent 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 consensus-based 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 finite-time analysis for the convergence of the distributed TD(0) algorithm. We do this when the communication network between the agents is time-varying 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.