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Preprint
Min-Max Optimization without Gradients: Convergence and Applications to Adversarial ML
arXiv.org
17 Jun 2020
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.
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Details
- Title
- Min-Max Optimization without Gradients: Convergence and Applications to Adversarial ML
- Creators
- Sijia LiuSongtao LuXiangyi ChenYao FengKaidi XuAbdullah Al-DujailiMinyi HongUna-May O'Reilly
- Publication Details
- arXiv.org
- Resource Type
- Preprint
- Language
- English
- Academic Unit
- Computer Science (Computing)
- Other Identifier
- 991021871469204721