{"id":5932,"date":"2025-08-08T07:03:03","date_gmt":"2025-08-08T07:03:03","guid":{"rendered":"https:\/\/mailitics.com\/index.php\/2025\/08\/08\/2508-05570\/"},"modified":"2025-08-08T07:03:03","modified_gmt":"2025-08-08T07:03:03","slug":"2508-05570","status":"publish","type":"post","link":"https:\/\/mailitics.com\/index.php\/2025\/08\/08\/2508-05570\/","title":{"rendered":"High-Order Error Bounds for Markovian LSA with Richardson-Romberg Extrapolation"},"content":{"rendered":"<p>    High-Order Error Bounds for Markovian LSA with Richardson-Romberg Extrapolation<br \/>\n \t<BR><br \/>\n<BR><\/BR><br \/>\n    <!-- no image --><br \/>\n \t<BR><br \/>\n<BR><\/BR><\/p>\n<div>arXiv:2508.05570v1 Announce Type: new<br \/>\nAbstract: In this paper, we study the bias and high-order error bounds of the Linear Stochastic Approximation (LSA) algorithm with Polyak-Ruppert (PR) averaging under Markovian noise. We focus on the version of the algorithm with constant step size $alpha$ and propose a novel decomposition of the bias via a linearization technique. We analyze the structure of the bias and show that the leading-order term is linear in $alpha$ and cannot be eliminated by PR averaging. To address this, we apply the Richardson-Romberg (RR) extrapolation procedure, which effectively cancels the leading bias term. We derive high-order moment bounds for the RR iterates and show that the leading error term aligns with the asymptotically optimal covariance matrix of the vanilla averaged LSA iterates.<\/div>\n<p> \t<BR><br \/>\n <BR><\/BR><br \/>\n    Ilya Levin, Alexey Naumov, Sergey Samsonov<br \/>\n \t<BR><br \/>\n<BR><\/BR><br \/>\n<a href=\"https:\/\/arxiv.org\/abs\/2508.05570\">Go to original source<\/a><br \/>\n \t<BR><br \/>\n <BR><\/BR><\/p>\n","protected":false},"excerpt":{"rendered":"<p>High-Order Error Bounds for Markovian LSA with Richardson-Romberg Extrapolation arXiv:2508.05570v1 Announce Type: new Abstract: In this paper, we study the bias and high-order error bounds of the Linear Stochastic Approximation (LSA) algorithm with Polyak-Ruppert (PR) averaging under Markovian noise. We focus on the version of the algorithm with constant step size $alpha$ and propose a [&hellip;]<\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[62,113,376,190,112,191],"tags":[2168,332,1424],"class_list":["post-5932","post","type-post","status-publish","format-standard","hentry","category-aimldsaimlds","category-cs-lg","category-math-oc","category-math-st","category-stat-ml","category-stat-th","tag-error","tag-high","tag-order"],"_links":{"self":[{"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/posts\/5932"}],"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=5932"}],"version-history":[{"count":0,"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/posts\/5932\/revisions"}],"wp:attachment":[{"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/media?parent=5932"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/categories?post=5932"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/tags?post=5932"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}