Zeroth-Order Stochastic Alternating Direction Method of Multipliers for Nonconvex Nonsmooth Optimization
Year: 2019
Type: conference-paper
Abstract: Alternating direction method of multipliers (ADMM) is a popular optimization tool for the composite and constrained problems in machine learning. However, in many machine learning problems such as black-box learning and bandit feedback, ADMM could fail because the explicit gradients of these problems are difficult or even infeasible to obtain. Zeroth-order (gradient-free) methods can effectively solve these problems due to that the objective function values are only required in the optimization. Recently, though there exist a few zeroth-order ADMM methods, they build on the convexity of objective function. Clearly, these existing zeroth-order methods are limited in many applications. In the paper, thus, we propose a class of fast zeroth-order stochastic ADMM methods (\emph{i.e.}, ZO-SVRG-ADMM and ZO-SAGA-ADMM) for solving nonconvex problems with multiple nonsmooth penalties, based on the coordinate smoothing gradient estimator. Moreover, we prove that both the ZO-SVRG-ADMM and ZO-SAGA-ADMM have convergence rate of $O(1/T)$, where $T$ denotes the number of iterations. In particular, our methods not only reach the best convergence rate of $O(1/T)$ for the nonconvex optimization, but also are able to effectively solve many complex machine learning problems with multiple regularized penalties and constraints. Finally, we conduct the experiments of black-box binary classification and structured adversarial attack on black-box deep neural network to validate the efficiency of our algorithms.
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: bronze
Awards: SCH: EXP: Collaborative Research: Privacy-Preserving Framework for Publishing Electronic Healthcare Records, G2241343584, BIGDATA: Collaborative Research: IA: Big Imaging-Omics Data Mining Framework for Precision Medicine, SCH: INT: New Machine Learning Framework to Conduct Anesthesia Risk Stratification and Decision Support for Precision Health, III: Medium: Collaborative Research: Robust Large-Scale Electronic Medical Record Data Mining Framework to Conduct Risk Stratification for Personalized Intervention, III: Small: Robust Large-Scale Data Mining for Knowledge Discovery in Depression Thought Records, BIGDATA: IA: Collaborative Research: Asynchronous Distributed Machine Learning Framework for Multi-Site Collaborative Brain Big Data Mining, 面向大数据机器学习的不确定性建模及应用研究, ABI Innovation: A New Automated Data Integration, Annotations, and Interaction Network Inference System for Analyzing Drosophila Gene Expression
OpenAlex ID: W2965124356