An Online Saddle Point optimization algorithm with Regularization

Abstract

This paper presents an online saddle-point optimization algorithm (OSP) to solve the optimal decision-making problem in economic games. In this setting, the two mutual competing players choose a pair of optimal decisions (Nash equilibrium) at each iteration. Firstly, the Follow the Leader (FTL) algorithm is proposed to update the decisions, and the regularization term is added to stabilize the Nash equilibrium for both players. Secondly, the saddle-point regret (SP-Regret) is used to measure the gap between the cumulative payoffs and the saddle point value of the aggregate payoff functions. To this end, this paper aims to minimize it. Finally, the simulation results show that, under the proposed OSP algorithm, the SP-Regret can still be sublinear with regularization and the decision variables of both players can be constrained to fluctuate within a certain range by adding regularization, which can effectively make the Nash equilibrium stable.