{"id":9884,"date":"2026-01-21T07:03:15","date_gmt":"2026-01-21T07:03:15","guid":{"rendered":"https:\/\/mailitics.com\/index.php\/2026\/01\/21\/2601-12238\/"},"modified":"2026-01-21T07:03:15","modified_gmt":"2026-01-21T07:03:15","slug":"2601-12238","status":"publish","type":"post","link":"https:\/\/mailitics.com\/index.php\/2026\/01\/21\/2601-12238\/","title":{"rendered":"On the Provable Suboptimality of Momentum SGD in Nonstationary Stochastic Optimization"},"content":{"rendered":"<p>    On the Provable Suboptimality of Momentum SGD in Nonstationary Stochastic Optimization<br \/>\n \t<BR><br \/>\n<BR><\/BR><br \/>\n    <!-- no image --><br \/>\n \t<BR><br \/>\n<BR><\/BR><\/p>\n<div>arXiv:2601.12238v1 Announce Type: new<br \/>\nAbstract: While momentum-based acceleration has been studied extensively in deterministic optimization problems, its behavior in nonstationary environments &#8212; where the data distribution and optimal parameters drift over time &#8212; remains underexplored. We analyze the tracking performance of Stochastic Gradient Descent (SGD) and its momentum variants (Polyak heavy-ball and Nesterov) under uniform strong convexity and smoothness in varying stepsize regimes. We derive finite-time bounds in expectation and with high probability for the tracking error, establishing a sharp decomposition into three components: a transient initialization term, a noise-induced variance term, and a drift-induced tracking lag. Crucially, our analysis uncovers a fundamental trade-off: while momentum can suppress gradient noise, it incurs an explicit penalty on the tracking capability. We show that momentum can substantially amplify drift-induced tracking error, with amplification that becomes unbounded as the momentum parameter approaches one, formalizing the intuition that using &#8216;stale&#8217; gradients hinders adaptation to rapid regime shifts. Complementing these upper bounds, we establish minimax lower bounds for dynamic regret under gradient-variation constraints. These lower bounds prove that the inertia-induced penalty is not an artifact of analysis but an information-theoretic barrier: in drift-dominated regimes, momentum creates an unavoidable &#8216;inertia window&#8217; that fundamentally degrades performance. Collectively, these results provide a definitive theoretical grounding for the empirical instability of momentum in dynamic environments and delineate the precise regime boundaries where SGD provably outperforms its accelerated counterparts.<\/div>\n<p> \t<BR><br \/>\n <BR><\/BR><br \/>\n    Sharan Sahu, Cameron J. Hogan, Martin T. Wells<br \/>\n \t<BR><br \/>\n<BR><\/BR><br \/>\n<a href=\"https:\/\/arxiv.org\/abs\/2601.12238\">Go to original source<\/a><br \/>\n \t<BR><br \/>\n <BR><\/BR><\/p>\n","protected":false},"excerpt":{"rendered":"<p>On the Provable Suboptimality of Momentum SGD in Nonstationary Stochastic Optimization arXiv:2601.12238v1 Announce Type: new Abstract: While momentum-based acceleration has been studied extensively in deterministic optimization problems, its behavior in nonstationary environments &#8212; where the data distribution and optimal parameters drift over time &#8212; remains underexplored. We analyze the tracking performance of Stochastic Gradient Descent [&hellip;]<\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[62,113,376,112],"tags":[1528,2754,1372],"class_list":["post-9884","post","type-post","status-publish","format-standard","hentry","category-aimldsaimlds","category-cs-lg","category-math-oc","category-stat-ml","tag-momentum","tag-sgd","tag-tracking"],"_links":{"self":[{"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/posts\/9884"}],"collection":[{"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/comments?post=9884"}],"version-history":[{"count":0,"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/posts\/9884\/revisions"}],"wp:attachment":[{"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/media?parent=9884"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/categories?post=9884"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/tags?post=9884"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}