Homogenization of Multi-agent Learning Dynamics in Finite-state Markov Games

Yann Kerzreho

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arXiv · 2506.21079

Homogenization of Multi-agent Learning Dynamics in Finite-state Markov Games

Yann Kerzreho

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Abstract

This paper introduces a new approach for approximating the learning dynamics of multiple reinforcement learning (RL) agents interacting in a finite-state Markov game. The idea is to rescale the learning process by simultaneously reducing the learning rate and increasing the update frequency, effectively treating the agent's parameters as a slow-evolving variable influenced by the fast-mixing game state. Under mild assumptions-ergodicity of the state process and continuity of the updates-we prove the convergence of this rescaled process to an ordinary differential equation (ODE). This ODE provides a tractable, deterministic approximation of the agent's learning dynamics. An implementation of the framework is available at\,: https://github.com/yannKerzreho/MarkovGameApproximation

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Yann Kerzreho. 2025-06-26. Homogenization of Multi-agent Learning Dynamics in Finite-state Markov Games. https://arxiv.org/abs/2506.21079

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