Online and Bandit Algorithms for Nonstationary Stochastic Saddle-Point Optimization
Abstract
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.
Cite
@article{arxiv.1912.01698,
title = {Online and Bandit Algorithms for Nonstationary Stochastic Saddle-Point Optimization},
author = {Abhishek Roy and Yifang Chen and Krishnakumar Balasubramanian and Prasant Mohapatra},
journal= {arXiv preprint arXiv:1912.01698},
year = {2019}
}