Distributed online bandit tracking for Nash equilibrium under partial-decision information setting

This paper is concerned with a Nash equilibrium (NE) tracking issue in online games with bandit feedback, where cost functions vary with time and agents only have access to the values of these functions at two points during each round. A partial-decision information setting is considered, in which agents have only access to the decisions of their neighbors. The primary objective of this paper is to develop a distributed online NE tracking algorithm that ensures sublinear growth of regret with respect to the total round T , under both the bandit feedback and partial-decision information setting. By utilizing a two-point estimator together with the leader-following consensus method, a new distributed online NE tracking algorithm is established with the estimated gradient and local estimated decisions based on the projection gradient-descent method. Moreover, sufficient conditions are derived to guarantee an improved upper bound of dynamic regret compared to existing bandit algorithms. Finally, a simulation example is presented to demonstrate the effectiveness of the proposed algorithm.