{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/zo-adamm-zeroth-order-adaptive-momentum","title":"ZO-AdaMM: Zeroth-Order Adaptive Momentum Method for Black-Box Optimization","arxiv_id":"1910.06513","date":"2019-10-15","proceeding":"NeurIPS 2019 12","authors":["Xiangyi Chen","Sijia Liu","Kaidi Xu","Xingguo Li","Xue Lin","Mingyi Hong","David Cox"],"abstract":"The adaptive momentum method (AdaMM), which uses past gradients to update descent directions and learning rates simultaneously, has become one of the most popular first-order optimization methods for solving machine learning problems. However, AdaMM is not suited for solving black-box optimization problems, where explicit gradient forms are difficult or infeasible to obtain. In this paper, we propose a zeroth-order AdaMM (ZO-AdaMM) algorithm, that generalizes AdaMM to the gradient-free regime. We show that the convergence rate of ZO-AdaMM for both convex and nonconvex optimization is roughly a factor of $O(\\sqrt{d})$ worse than that of the first-order AdaMM algorithm, where $d$ is problem size. In particular, we provide a deep understanding on why Mahalanobis distance matters in convergence of ZO-AdaMM and other AdaMM-type methods. As a byproduct, our analysis makes the first step toward understanding adaptive learning rate methods for nonconvex constrained optimization. Furthermore, we demonstrate two applications, designing per-image and universal adversarial attacks from black-box neural networks, respectively. We perform extensive experiments on ImageNet and empirically show that ZO-AdaMM converges much faster to a solution of high accuracy compared with $6$ state-of-the-art ZO optimization methods.","url_abs":"https://arxiv.org/abs/1910.06513v2","url_pdf":"https://arxiv.org/pdf/1910.06513v2.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"abstracts"},"code_links":[{"paper_slug":"zo-adamm-zeroth-order-adaptive-momentum","repo_url":"https://github.com/KaidiXu/ZO-AdaMM","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"tf","reach":{"status":"ok"}}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":"https://syntology.ai/paper/1910.06513","atlas_url":"https://app.syntology.ai/?focus=1910.06513","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}