Two trust region type algorithms for solving nonconvex-strongly concave minimax problems

arXiv:2402.09807v1 Announce Type: cross
Abstract: In this paper, we propose a Minimax Trust Region (MINIMAX-TR) algorithm and a Minimax Trust Region Algorithm with Contractions and Expansions(MINIMAX-TRACE) algorithm for solving nonconvex-strongly concave minimax problems. Both algorithms can find an $(\epsilon, \sqrt{\epsilon})$-second order stationary point(SSP) within $\mathcal{O}(\epsilon^{-1.5})$ iterations, which matches the best well known iteration complexity.

abstract algorithm algorithms arxiv cs.lg math.oc minimax paper stat.ml trust type