A Single-Loop Smoothed Gradient Descent-Ascent Algorithm for Nonconvex-Concave Min-Max Problems

• URL: http://arxiv.org/abs/2010.15768v2
• Date: Mon, 4 Jul 2022 23:17:33 GMT
• Title: A Single-Loop Smoothed Gradient Descent-Ascent Algorithm for Nonconvex-Concave Min-Max Problems
• Authors: Jiawei Zhang, Peijun Xiao, Ruoyu Sun and Zhi-Quan Luo
• Abstract summary: Non-con-max problem arises in many applications including minimizing a pointwise set of non functions to solve this robust problem. A.A. algorithm can achieve an $(/A-O-) of $(/A-O-)$ for a finite collection of non functions.
• Score: 33.83671897619922
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Nonconvex-concave min-max problem arises in many machine learning applications including minimizing a pointwise maximum of a set of nonconvex functions and robust adversarial training of neural networks. A popular approach to solve this problem is the gradient descent-ascent (GDA) algorithm which unfortunately can exhibit oscillation in case of nonconvexity. In this paper, we introduce a "smoothing" scheme which can be combined with GDA to stabilize the oscillation and ensure convergence to a stationary solution. We prove that the stabilized GDA algorithm can achieve an $O(1/\epsilon^2)$ iteration complexity for minimizing the pointwise maximum of a finite collection of nonconvex functions. Moreover, the smoothed GDA algorithm achieves an $O(1/\epsilon^4)$ iteration complexity for general nonconvex-concave problems. Extensions of this stabilized GDA algorithm to multi-block cases are presented. To the best of our knowledge, this is the first algorithm to achieve $O(1/\epsilon^2)$ for a class of nonconvex-concave problem. We illustrate the practical efficiency of the stabilized GDA algorithm on robust training.

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