Two trust region type algorithms for solving nonconvex-strongly concave minimax problems
This work addresses optimization challenges in minimax problems, which are incremental improvements for researchers in optimization and machine learning.
The paper tackles nonconvex-strongly concave minimax problems by proposing two trust region algorithms, MINIMAX-TR and MINIMAX-TRACE, achieving an iteration complexity of O(ε^{-1.5}) to find an (ε, √ε)-second order stationary point, matching the best known bound.
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 $(ε, \sqrtε)$-second order stationary point(SSP) within $\mathcal{O}(ε^{-1.5})$ iterations, which matches the best well known iteration complexity.