Global Convergence of Localized Policy Iteration in Networked Multi-Agent Reinforcement Learning

TL;DR

This paper introduces a Localized Policy Iteration algorithm for multi-agent reinforcement learning over networks, achieving near-global optimality with local information and demonstrating finite-sample convergence.

Contribution

The paper proposes a novel LPI algorithm that ensures convergence to near-optimal policies using only local neighborhood information in networked MARL.

Findings

LPI learns policies with an optimality gap decaying polynomially in neighborhood size.

Finite-sample convergence of LPI to the global optimum is established.

Numerical simulations confirm the effectiveness of the proposed method.

Abstract

We study a multi-agent reinforcement learning (MARL) problem where the agents interact over a given network. The goal of the agents is to cooperatively maximize the average of their entropy-regularized long-term rewards. To overcome the curse of dimensionality and to reduce communication, we propose a Localized Policy Iteration (LPI) algorithm that provably learns a near-globally-optimal policy using only local information. In particular, we show that, despite restricting each agent's attention to only its $\kappa$-hop neighborhood, the agents are able to learn a policy with an optimality gap that decays polynomially in $\kappa$. In addition, we show the finite-sample convergence of LPI to the global optimal policy, which explicitly captures the trade-off between optimality and computational complexity in choosing $\kappa$. Numerical simulations demonstrate the effectiveness of LPI.