{"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/on-the-insufficiency-of-existing-momentum","title":"On the insufficiency of existing momentum schemes for Stochastic Optimization","arxiv_id":"1803.05591","date":"2018-03-15","proceeding":"ICLR 2018 1","authors":["Rahul Kidambi","Praneeth Netrapalli","Prateek Jain","Sham M. Kakade"],"abstract":"Momentum based stochastic gradient methods such as heavy ball (HB) and\nNesterov's accelerated gradient descent (NAG) method are widely used in\npractice for training deep networks and other supervised learning models, as\nthey often provide significant improvements over stochastic gradient descent\n(SGD). Rigorously speaking, \"fast gradient\" methods have provable improvements\nover gradient descent only for the deterministic case, where the gradients are\nexact. In the stochastic case, the popular explanations for their wide\napplicability is that when these fast gradient methods are applied in the\nstochastic case, they partially mimic their exact gradient counterparts,\nresulting in some practical gain. This work provides a counterpoint to this\nbelief by proving that there exist simple problem instances where these methods\ncannot outperform SGD despite the best setting of its parameters. These\nnegative problem instances are, in an informal sense, generic; they do not look\nlike carefully constructed pathological instances. These results suggest (along\nwith empirical evidence) that HB or NAG's practical performance gains are a\nby-product of mini-batching.\n  Furthermore, this work provides a viable (and provable) alternative, which,\non the same set of problem instances, significantly improves over HB, NAG, and\nSGD's performance. This algorithm, referred to as Accelerated Stochastic\nGradient Descent (ASGD), is a simple to implement stochastic algorithm, based\non a relatively less popular variant of Nesterov's Acceleration. Extensive\nempirical results in this paper show that ASGD has performance gains over HB,\nNAG, and SGD.","url_abs":"http://arxiv.org/abs/1803.05591v2","url_pdf":"http://arxiv.org/pdf/1803.05591v2.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":"on-the-insufficiency-of-existing-momentum","repo_url":"https://github.com/rahulkidambi/AccSGD","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"pytorch","reach":{"status":"ok"}},{"paper_slug":"on-the-insufficiency-of-existing-momentum","repo_url":"https://github.com/severilov/A2Grad_optimizer","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"pytorch","reach":{"status":"ok"}}],"tasks":[{"task_slug":"stochastic-optimization","task_name":"Stochastic Optimization"}],"methods":[{"method_slug":"sgd","method_name":"SGD"}],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":"https://syntology.ai/paper/1803.05591","atlas_url":"https://app.syntology.ai/?focus=1803.05591","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}