In this paper, we study zeroth-order algorithms for nonconvex-concave minimax problems, which have attracted widely attention in machine learning, signal processing and many other fields in recent years. We propose a zeroth-order alternating randomized gradient projection (ZO-AGP) algorithm for smooth nonconvex-concave minimax problems, and its iteration complexity to obtain an $\varepsilon$-stationary point is bounded by $\mathcal{O}(\varepsilon^{-4})$, and the number of function value estimation is bounded by $\mathcal{O}(d_{x}\varepsilon^{-4}+d_{y}\varepsilon^{-6})$ per iteration. Moreover, we propose a zeroth-order block alternating randomized proximal gradient algorithm (ZO-BAPG) for solving block-wise nonsmooth nonconvex-concave minimax optimization problems, and the iteration complexity to obtain an $\varepsilon$-stationary point is bounded by $\mathcal{O}(\varepsilon^{-4})$ and the number of function value estimation per iteration is bounded by $\mathcal{O}(K d_{x}\varepsilon^{-4}+d_{y}\varepsilon^{-6})$. To the best of our knowledge, this is the first time that zeroth-order algorithms with iteration complexity gurantee are developed for solving both general smooth and block-wise nonsmooth nonconvex-concave minimax problems. Numerical results on data poisoning attack problem validate the efficiency of the proposed algorithms.
翻译:在本文中, 我们研究的是用于非convex- concave minimax 问题的零顺序算法, 近些年来, 这些问题在机器学习、 信号处理和其他许多字段中引起了广泛的关注。 我们提出一个用于平滑的非convex 迷你轴问题的零顺序交替随机梯度投影( ZO- AGP) 算法( ZO- AGP) 。 此外, 我们提出一个零顺序交替随机的 rootalal roadal cale log (ZO- BAGP), 以获得块非mothcalalal { O} (\\ varepremox liclation{O} 函数中, 用于解决块状的非cal- mostal- mocial $n- deal- devocial_ ral_ knational ral_ ral_ lax lax lax lax lax pal lax lax pal- pal dal dal_ lax disal_ dal_ knal_ lax disal_ knal=x pal=xx pal=xxxxx pal=xl=xxxxxxxxxxxxxxxxxxl=xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx