Distributed Online Optimization for Two-network Zero-sum Games Under Communication Constraints

This paper investigates the distributed optimization problem in two-network zero-sum games, where the two networks represent two opposing players. Each network consists of a set of agents with time-varying cost functions, and the agents optimize the payoff of their network in the game through communication and collaboration. Considering the two communication constrained situations in real optimization scenarios, namely, limited communication resources and limited information feedback, a distributed online optimization algorithm based on event-triggered communication and two-point Bandit feedback is designed, and the performance of the algorithm is evaluated using the dynamic Nash equilibrium regret. Under certain assumptions, a sublinear dynamic Nash equilibrium regret bound relative to the total number of game iterations is established, thereby validating the effectiveness of the algorithm. Additionally, the designed algorithm is extended to a multi-epoch version, and a sublinear dynamic Nash equilibrium regret bound is also established. Finally, a simulation example involving a bilinear matrix game is provided to further verify the performance of the two designed algorithms.