  Decentralized online learning for seeking generalized Nash equilibrium (GNE)
of noncooperative games in dynamic environments is studied in this paper. Each
player aims at selfishly minimizing its own time-varying cost function subject
to time-varying coupled constraints and local feasible set constraints. Only
local cost functions and local constraints are available to individual players,
who can receive their neighbors' information through a fixed and connected
graph. In addition, players have no prior knowledge of cost functions and local
constraint functions in the future time. In this setting, a novel distributed
online learning algorithm for seeking GNE of the studied game is devised based
on mirror descent and a primal-dual strategy. It is shown that the presented
algorithm can achieve sublinearly bounded dynamic regrets and constraint
violation by appropriately choosing decreasing stepsizes. Finally, the obtained
theoretical result is corroborated by a numerical simulation.
