Zeroth-Order Optimization for Composite Problems with Functional Constraints

Abstract

In many real-world problems, first-order (FO) derivative evaluations are too expensive or even inaccessible. For solving these problems, zeroth-order (ZO) methods that only need function evaluations are often more efficient than FO methods or sometimes the only options. In this paper, we propose a novel zeroth-order inexact augmented Lagrangian method (ZO-iALM) to solve black-box optimization problems, which involve a composite (i.e., smooth+nonsmooth) objective and functional constraints. This appears to be the first work that develops an iALM-based ZO method for functional constrained optimization and meanwhile achieves query complexity results matching the best-known FO complexity results up to a factor of variable dimension. With an extensive experimental study, we show the effectiveness of our method. The applications of our method span from classical optimization problems to practical machine learning examples such as resource allocation in sensor networks and adversarial example generation.

Understanding and improving zeroth-order optimization methods on AI-driven molecule optimization

“…9 Many types of ZO optimization algorithms have been developed, including the ZO gradient descent (ZO-GD), 10 ZO sign-based gradient descent (ZO-signGD), 11 ZO adaptive momentum method (ZO-AdaMM, or ZO-Adam specifically for the Adam variant), 12 and more. 13,14 The optimality of ZO optimization methods has also been studied under given problem assumptions. 15 ZO optimization methods have achieved impressive feats in adversarial machine learning, where they have been used for adversarial example generation in black-box settings and demonstrated comparable success to first-order white-box attacks.…”