Experience-replay Innovative Dynamics

TL;DR

This paper introduces a novel multi-agent reinforcement learning algorithm based on innovative dynamics like BNN and Smith, which can potentially improve convergence properties beyond traditional replicator dynamics, supported by theoretical and empirical evidence.

Contribution

The paper develops a new MARL algorithm using experience replay and revision protocols that emulate innovative dynamics, extending theoretical guarantees beyond replicator dynamics.

Findings

The algorithm's trajectories can be tuned to match innovative dynamics behaviors.

Theoretical framework extends convergence guarantees for MARL.

Empirical results validate the theoretical insights.

Abstract

Despite its groundbreaking success, multi-agent reinforcement learning (MARL) still suffers from instability and nonstationarity. Replicator dynamics, the most well-known model from evolutionary game theory (EGT), provide a theoretical framework for the convergence of the trajectories to Nash equilibria and, as a result, have been used to ensure formal guarantees for MARL algorithms in stable game settings. However, they exhibit the opposite behavior in other settings, which poses the problem of finding alternatives to ensure convergence. In contrast, innovative dynamics, such as the Brown-von Neumann-Nash (BNN) or Smith, result in periodic trajectories with the potential to approximate Nash equilibria. Yet, no MARL algorithms based on these dynamics have been proposed. In response to this challenge, we develop a novel experience replay-based MARL algorithm that incorporates revision protocols as tunable hyperparameters. We demonstrate, by appropriately adjusting the revision protocols, that the behavior of our algorithm mirrors the trajectories resulting from these dynamics. Importantly, our contribution provides a framework capable of extending the theoretical guarantees of MARL algorithms beyond replicator dynamics. Finally, we corroborate our theoretical findings with empirical results.