Fictitious Mean-field Reinforcement Learning for Distributed Load Balancing

Abstract

In this work, we study the application of multi-agent reinforcement learning (RL) in distributed systems. In particular, we consider a setting in which strategic clients compete over a set of heterogeneous servers. Each client receives jobs at a fixed rate. For each job, clients choose a server to run the job. The objective of each client is to minimize its average wait time. We model this setting as a Markov game and theoretically prove that the game becomes in the limit a Markov potential game (MPG). We further propose a novel mean-field reinforcement learning algorithm, combining mean-field Q-learning and fictitious play. Through rigorous experiments, we show that our algorithm outperforms naive deployment of single-agent RL, and in some cases, performs comparably to the Nash Q-learning, while being less complex in terms of memory and computation. We also empirically analyze the convergence of our proposed algorithm to a Nash equilibrium and study its performance in four benchmark examples.