Abstract:

In this paper, we propose a mirror descent gradient ascent algorithm to solve one side relatively smooth nonconvex-concave minimax optimization problems. At each iteration of the proposed algorithm, a mirror descent step is performed to update the relatively smooth variable, while a gradient ascent projection step is used to update the smooth variable alternately. We also prove that the iteration complexity of the proposed algorithm is $\mathcal{O}\left( \varepsilon ^{-4} \right)$ to achieve an $\varepsilon$-approximate first-order stationary point.

Key words: nonconvex-concave minimax optimization problem, relatively smooth, mirror gradient method