Online and Bandit Algorithms for Nonstationary Stochastic Saddle-Point Optimization
This work addresses nonstationary optimization problems for applications in game theory and machine learning, representing an incremental advancement.
The authors tackled nonstationary stochastic saddle-point optimization in online and bandit settings by proposing regret notions and analyzing extragradient and Frank-Wolfe algorithms, achieving sub-linear regret bounds.
Saddle-point optimization problems are an important class of optimization problems with applications to game theory, multi-agent reinforcement learning and machine learning. A majority of the rich literature available for saddle-point optimization has focused on the offline setting. In this paper, we study nonstationary versions of stochastic, smooth, strongly-convex and strongly-concave saddle-point optimization problem, in both online (or first-order) and multi-point bandit (or zeroth-order) settings. We first propose natural notions of regret for such nonstationary saddle-point optimization problems. We then analyze extragradient and Frank-Wolfe algorithms, for the unconstrained and constrained settings respectively, for the above class of nonstationary saddle-point optimization problems. We establish sub-linear regret bounds on the proposed notions of regret in both the online and bandit setting.