Online distributed algorithms for aggregative games with stochastic costs over time-varying networks

In this paper, the online aggregative games in dynamic environments are studied, where each player's goal is to seek the time-varying Nash equilibria in a distributed manner. Different from the existing works on aggregative games, here the cost functions are considered to be stochastic. In this problem, each player only has access to noisy gradients of its own cost function in the past time and can only communicate with its immediate neighbours through a time-varying digraph. To handle this problem, we propose an online distributed stochastic algorithm based on the projection method and the average tracking strategy. Of particular interest is that the high probability bound of the dynamic regrets is established to guarantee the performance of the algorithm. The result shows that if the variation in the Nash equilibrium sequence is within a certain range, then the regret have a sublinear bound with high probability. Finally, the validity of the theoretical results is verified by a simulation example.