{"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/convergence-and-complexity-of-stochastic","title":"Stochastic regularized majorization-minimization with weakly convex and multi-convex surrogates","arxiv_id":"2201.01652","date":"2022-01-05","proceeding":null,"authors":["Hanbaek Lyu"],"abstract":"Stochastic majorization-minimization (SMM) is a class of stochastic optimization algorithms that proceed by sampling new data points and minimizing a recursive average of surrogate functions of an objective function. The surrogates are required to be strongly convex and convergence rate analysis for the general non-convex setting was not available. In this paper, we propose an extension of SMM where surrogates are allowed to be only weakly convex or block multi-convex, and the averaged surrogates are approximately minimized with proximal regularization or block-minimized within diminishing radii, respectively. For the general nonconvex constrained setting with non-i.i.d. data samples, we show that the first-order optimality gap of the proposed algorithm decays at the rate $O((\\log n)^{1+\\epsilon}/n^{1/2})$ for the empirical loss and $O((\\log n)^{1+\\epsilon}/n^{1/4})$ for the expected loss, where $n$ denotes the number of data samples processed. Under some additional assumption, the latter convergence rate can be improved to $O((\\log n)^{1+\\epsilon}/n^{1/2})$. As a corollary, we obtain the first convergence rate bounds for various optimization methods under general nonconvex dependent data setting: Double-averaging projected gradient descent and its generalizations, proximal point empirical risk minimization, and online matrix/tensor decomposition algorithms. We also provide experimental validation of our results.","url_abs":"https://arxiv.org/abs/2201.01652v3","url_pdf":"https://arxiv.org/pdf/2201.01652v3.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":"convergence-and-complexity-of-stochastic","repo_url":"https://github.com/HanbaekLyu/SRMM","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"pytorch","reach":{"status":"ok"}}],"tasks":[{"task_slug":"dictionary-learning","task_name":"Dictionary Learning"},{"task_slug":"image-deep-networks","task_name":"Image Deep Networks"},{"task_slug":"stochastic-optimization","task_name":"Stochastic Optimization"},{"task_slug":"tensor-decomposition","task_name":"Tensor Decomposition"}],"methods":[{"method_slug":"amsgrad","method_name":"AMSGrad"},{"method_slug":"adagrad","method_name":"AdaGrad"},{"method_slug":"adam","method_name":"Adam"},{"method_slug":"sgd","method_name":"SGD"},{"method_slug":"srmm","method_name":"SRMM"}],"datasets_introduced":[],"methods_introduced":[{"slug":"srmm","name":"SRMM","full_name":"Stochastic Regularized Majorization-Minimization"}],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=2201.01652","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}