A Distributed Nesterov’s Approach for Fast Nash Equilibrium Seeking in Noncooperative Games
摘要
In this paper, the author is concerned with the problem of achieving Nash equilibrium in noncooperative games over networks. The author proposes two types of distributed projected gradient dynamics with accelerated convergence rates. The first type is a variant of the commonly-known consensus-based gradient dynamics, where the consensual terms for determining the actions of each player are discarded to accelerate the learning process. The second type is formulated by introducing the Nesterov’s accelerated method into the distributed projected gradient dynamics. The author proves convergence of both algorithms with at least linear rates under the common assumption of Lipschitz continuity and strongly monotonicity. Simulation examples are presented to validate the outperformance of the proposed algorithms over the well-known consensus-based approach and augmented game based approach. It is shown that the required number of iterations to reach the Nash equilibrium is greatly reduced in the proposed algorithms. These results could be helpful to address the issue of long convergence time in partial-information Nash equilibrium seeking algorithms.