Online Parameter Identification of Generalized Non-cooperative Game
Jianguo Chen Jinlong Lei Hongsheng Qi Yiguang Hong
This work studies the parameter identification problem of a generalized
non-cooperative game, where each player's cost function is influenced by an
observable signal and some unknown parameters. We consider the scenario where
equilibrium of the game at some observable signals can be observed with noises,
whereas our goal is to identify the unknown parameters with the observed data.
Assuming that the observable signals and the corresponding noise-corrupted
equilibriums are acquired sequentially, we construct this parameter
identification problem as online optimization and introduce a novel online
parameter identification algorithm. To be specific, we construct a regularized
loss function that balances conservativeness and correctiveness, where the
conservativeness term ensures that the new estimates do not deviate
significantly from the current estimates, while the correctiveness term is
captured by the Karush-Kuhn-Tucker conditions. We then prove that when the
players' cost functions are linear with respect to the unknown parameters and
the learning rate of the online parameter identification algorithm satisfies
\mu_k \propto 1/\sqrt{k}, along with other assumptions, the regret bound of the
proposed algorithm is O(\sqrt{K}). Finally, we conduct numerical simulations on
a Nash-Cournot problem to demonstrate that the performance of the online
identification algorithm is comparable to that of the offline setting.