时变有向图上的差分隐私分布式纳什均衡求解
Differentially Private Distributed Nash Equilibrium Seeking over Time-Varying Digraphs
AI总结：
该研究针对时变非平衡有向图下的聚合博弈，提出注入拉普拉斯噪声、结合push-sum协议与衰减因子、动量项的差分隐私分布式纳什均衡求解算法，实现收敛性与差分隐私的兼顾，仿真验证了有效性。
摘要：
本文针对时变非平衡有向通信图下的聚合博弈，提出了一种新的差分隐私分布式纳什均衡求解算法。该算法向传输信息中注入独立随机拉普拉斯噪声，以保护参与者的敏感信息。随后，利用push-sum（推送和）一致性协议，基于时变拓扑下的受扰信息估计聚合函数。算法设计了衰减因子和动量项，分别用于减弱噪声的负面影响并保证算法的收敛性。本文证明该算法可实现几乎必然收敛，同时在有限累积隐私预算下具备严格的差分隐私保障，无需在可证明收敛性与差分隐私之间进行权衡。最后，通过仿真实验验证了所提算法的有效性。
英文摘要：
This paper proposes a new differentially private distributed Nash equilibrium seeking algorithm for aggregative games under time-varying unbalanced directed communication graphs. Random independent Laplace noises are injected into the transmitted information to protect players' sensitive information. Then, the push-sum consensus protocol is utilized to estimate the aggregate function with the perturbed information under the time-varying topologies. The weakening factor and the momentum term are designed to attenuate the negative affect of the noise and guarantee the convergence of the algorithm, respectively. The algorithm is then proven to ensure the almost sure convergence, as well as rigorous differential privacy with a finite cumulative privacy budget, without requiring a trade-off between provable convergence and differential privacy. Finally, the simulation is provided to demonstrate the effectiveness of the proposed algorithm.
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