A Potential Game Perspective in Federated Learning

TL;DR

This paper models federated learning as a potential game where clients independently choose efforts, analyzing equilibrium existence, uniqueness, and optimal rewards to improve training outcomes.

Contribution

It introduces a potential game framework for federated learning, analyzing equilibrium properties and identifying optimal reward strategies for better client efforts.

Findings

Existence of Nash equilibria in the proposed game

Uniqueness of equilibrium in homogeneous settings

Optimal reward factor improves client efforts

Abstract

Federated learning (FL) is an emerging paradigm for training machine learning models across distributed clients. Traditionally, in FL settings, a central server assigns training efforts (or strategies) to clients. However, from a market-oriented perspective, clients may independently choose their training efforts based on rational self-interest. To explore this, we propose a potential game framework where each client's payoff is determined by their individual efforts and the rewards provided by the server. The rewards are influenced by the collective efforts of all clients and can be modulated through a reward factor. Our study begins by establishing the existence of Nash equilibria (NEs), followed by an investigation of uniqueness in homogeneous settings. We demonstrate a significant improvement in clients' training efforts at a critical reward factor, identifying it as the optimal choice for the server. Furthermore, we prove the convergence of the best-response algorithm to compute NEs for our FL game. Finally, we apply the training efforts derived from specific NEs to a real-world FL scenario, validating the effectiveness of the identified optimal reward factor.