Independent Policy Mirror Descent for Markov Potential Games: Scaling to Large Number of Players

TL;DR

This paper introduces an independent policy mirror descent algorithm for Markov Potential Games, achieving improved scalability with a square root dependence on the number of agents, suitable for large multi-agent systems.

Contribution

It demonstrates that natural policy gradient with KL regularization improves iteration complexity dependence on the number of agents in MPGs.

Findings

Iteration complexity scales as √N with natural policy gradient.

Complexity is independent of action space size.

Improves over prior linear dependence results.

Abstract

Markov Potential Games (MPGs) form an important sub-class of Markov games, which are a common framework to model multi-agent reinforcement learning problems. In particular, MPGs include as a special case the identical-interest setting where all the agents share the same reward function. Scaling the performance of Nash equilibrium learning algorithms to a large number of agents is crucial for multi-agent systems. To address this important challenge, we focus on the independent learning setting where agents can only have access to their local information to update their own policy. In prior work on MPGs, the iteration complexity for obtaining $\epsilon$-Nash regret scales linearly with the number of agents $N$. In this work, we investigate the iteration complexity of an independent policy mirror descent (PMD) algorithm for MPGs. We show that PMD with KL regularization, also known as natural policy gradient, enjoys a better $\sqrt{N}$ dependence on the number of agents, improving over PMD with Euclidean regularization and prior work. Furthermore, the iteration complexity is also independent of the sizes of the agents' action spaces.