Mean-Field Games Enhance Federated Learning Privacy

Federated learning (FL) enables collaborative AI model training across distributed clients without centralizing sensitive data, yet privacy remains a significant concern due to potential information leakage from shared model updates. Existing privacy-preserving methods either inject noise, which can limit guarantees, or model client privacy choices as a multi-agent game, which becomes computationally intractable with a large number of clients. This paper bridges these approaches by formulating privacy-preserving federated learning as a mean-field privacy game. In this framework, each client independently and strategically selects its own privacy budget, interacting with the broader population only through a single, aggregate mean-field statistic. This mean-field limit provides a tractable equilibrium even for an arbitrary number of clients, accommodating diverse client preferences. The framework also inherits an exponentially decaying privacy guarantee through a log-Sobolev contraction. It generalizes existing methods, recovering the entropic privacy baseline as a homogeneous special case and the multi-agent privacy game for finite populations. Experiments on quadratic regression, logistic regression, and MNIST datasets demonstrate that this proposed framework achieves the same privacy-utility trade-off as the entropic baseline while delivering personalized privacy guarantees that homogeneous baselines cannot provide.