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In this paper, we consider a class of nonconvex-nonconcave minimax problems,i.e., NC-PL minimax problems, whose objective functions satisfy the Polyak-\Lojasiewicz (PL) condition with respect to the inner variable. We propose azeroth-order alternating gradient descent ascent (ZO-AGDA) algorithm and azeroth-order variance reduced alternating gradient descent ascent (ZO-VRAGDA)algorithm for solving NC-PL minimax problem under the deterministic and thestochastic setting, respectively. The total number of function value queries toobtain an $\epsilon$-stationary point of ZO-AGDA and ZO-VRAGDA algorithm forsolving NC-PL minimax problem is upper bounded by$\mathcal{O}(\varepsilon^{-2})$ and $\mathcal{O}(\varepsilon^{-3})$,respectively. To the best of our knowledge, they are the first two zeroth-orderalgorithms with the iteration complexity gurantee for solving NC-PL minimaxproblems.

Zeroth-Order Alternating Gradient Descent Ascent Algorithms for a Class of Nonconvex-Nonconcave Minimax Problems