Min-Max Optimization without Gradients: Convergence and Applications to Adversarial ML

Sijia Liu, Songtao Lu, Xiangyi Chen, Yao Feng, Kaidi Xu, Abdullah Al-Dujaili, Minyi Hong, Una-May Obelilly

TL;DR: Towards principled and efficient black-box min-max optimization with applications to design of evasion and poisoning adversarial attacks

Abstract: In this paper, we study the problem of constrained robust (min-max) optimization ina black-box setting, where the desired optimizer cannot access the gradients of the objective function but may query its values. We present a principled optimization framework, integrating a zeroth-order (ZO) gradient estimator with an alternating projected stochastic gradient descent-ascent method, where the former only requires a small number of function queries and the later needs just one-step descent/ascent update. We show that the proposed framework, referred to as ZO-Min-Max, has a sub-linear convergence rate under mild conditions and scales gracefully with problem size. From an application side, we explore a promising connection between black-box min-max optimization and black-box evasion and poisoning attacks in adversarial machine learning (ML). Our empirical evaluations on these use cases demonstrate the effectiveness of our approach and its scalability to dimensions that prohibit using recent black-box solvers.

Keywords: nonconvex optimization, min-max optimization, robust optimization, adversarial attack

Community Implementations: [ 1 code implementation](https://www.catalyzex.com/paper/arxiv:1909.13806/code)