Nonconvex Zeroth-Order Stochastic ADMM Methods with Lower Function Query Complexity

• URL: http://arxiv.org/abs/1907.13463v4
• Date: Mon, 11 Dec 2023 06:13:15 GMT
• Title: Nonconvex Zeroth-Order Stochastic ADMM Methods with Lower Function Query Complexity
• Authors: Feihu Huang, Shangqian Gao, Jian Pei and Heng Huang
• Abstract summary: Zeroth-order (a.k.a, derivative-free) methods are a class of effective optimization methods for solving machine learning problems. In this paper, we propose a class faster faster zerothorder alternating gradient method multipliers (MMADMM) to solve the non finitesum problems. We show that ZOMMAD methods can achieve a lower function $O(frac13nfrac1)$ for finding an $epsilon$-stationary point. At the same time, we propose a class faster zerothorder online ADM methods (M
• Score: 109.54166127479093
• License: http://creativecommons.org/licenses/by-nc-sa/4.0/
• Abstract: Zeroth-order (a.k.a, derivative-free) methods are a class of effective optimization methods for solving complex machine learning problems, where gradients of the objective functions are not available or computationally prohibitive. Recently, although many zeroth-order methods have been developed, these approaches still have two main drawbacks: 1) high function query complexity; 2) not being well suitable for solving the problems with complex penalties and constraints. To address these challenging drawbacks, in this paper, we propose a class of faster zeroth-order stochastic alternating direction method of multipliers (ADMM) methods (ZO-SPIDER-ADMM) to solve the nonconvex finite-sum problems with multiple nonsmooth penalties. Moreover, we prove that the ZO-SPIDER-ADMM methods can achieve a lower function query complexity of $O(nd+dn^{\frac{1}{2}}\epsilon^{-1})$ for finding an $\epsilon$-stationary point, which improves the existing best nonconvex zeroth-order ADMM methods by a factor of $O(d^{\frac{1}{3}}n^{\frac{1}{6}})$, where $n$ and $d$ denote the sample size and data dimension, respectively. At the same time, we propose a class of faster zeroth-order online ADMM methods (ZOO-ADMM+) to solve the nonconvex online problems with multiple nonsmooth penalties. We also prove that the proposed ZOO-ADMM+ methods achieve a lower function query complexity of $O(d\epsilon^{-\frac{3}{2}})$, which improves the existing best result by a factor of $O(\epsilon^{-\frac{1}{2}})$. Extensive experimental results on the structure adversarial attack on black-box deep neural networks demonstrate the efficiency of our new algorithms.

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