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.

本文研究了黑盒环境下有约束的鲁棒（最小 - 最大）优化问题，并采用了零阶梯度估计器与交替投影随机梯度下降 - 上升方法的优化框架，称为 ZO-Min-Max，旨在探索在对抗机器学习中的黑盒最小 - 最大优化与黑盒逃避和污染攻击之间的可能联系。实证评估表明了该方法的有效性和可扩展性。