研究联邦学习中客户端理性选择训练努力的非线性均衡转变。
Nonlinear Equilibrium Transitions in a Potential Game Model for Federated Learning
- 用潜在博弈建模客户端自利行为与服务器奖励的关系。
- 发现奖励因子在临界值处导致努力水平跳变，出现多均衡。
- 适合关注联邦学习激励机制设计的研究者参考。
在联邦学习中，通常由中心服务器分配训练资源。但从市场视角看，客户端可能基于自身利益自主决定训练努力。为此，我们提出一种潜在博弈框架，其中每个客户端的收益由其个人努力及服务器提供的奖励共同决定，而奖励受所有客户端集体努力影响，并可通过奖励因子调节。我们首先证明了纳什均衡（NE）的存在性，接着在静态设定下研究其唯一性。结果显示，均衡依赖于奖励因子的非线性关系，在临界值处因势函数失去严格凸性，导致均衡不唯一，并在低努力与高努力分支间发生突变。此外，我们证明了最优响应算法在该博弈中的收敛性。最后，将从均衡中推导出的客户端理性努力应用于多种数据集和模型的联邦学习训练，验证了关键奖励因子的有效性。
原文摘要 · Abstract (English)
In federated learning (FL), a central server typically allocates training efforts to clients. However, from a market-oriented perspective, clients may independently choose their training efforts based on rational self-interest. To study this setting, we propose a potential game framework in which each client's payoff is determined by its individual effort and the rewards provided by the server. The rewards are influenced by the collective efforts of all clients and can be modulated by a reward factor. We first establish the existence of Nash equilibria (NEs) and then investigate their uniqueness in a stationary setting. We show that the NEs depend nonlinearly on the reward factor and exhibit a nonsmooth transition at a critical value, where the stationary potential loses strict curvature, leading to nonunique NEs and a jump between low-effort and high-effort branches. Furthermore, we prove the convergence of the best-response algorithm for computing NEs in our FL game. Finally, we apply the clients' rational efforts derived from the NEs to FL training with various datasets and models, thereby validating the effectiveness of the identified critical reward factor.
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