Statistical Privacy-Preserving Distributed Online Aggregative Games via Mirror Descent with Correlated Perturbations

Distributed online aggregative games are widely used to model sequential decision-making problems in dynamic networked systems. However, the repeated information exchange required by distributed algorithms may disclose players’ sensitive local data. This paper investigates a privacy-preserving distributed online aggregative game over multi-agent networks. A distributed online mirror descent algorithm with correlated perturbations is developed to protect local private information. Under standard assumptions, an expected dynamic regret bound and a statistical privacy guarantee are established for the proposed algorithm. Numerical results demonstrate the effectiveness of the proposed algorithm and reveal the tradeoff between privacy protection and algorithmic performance.