{"id":8302,"date":"2025-11-12T07:03:15","date_gmt":"2025-11-12T07:03:15","guid":{"rendered":"https:\/\/mailitics.com\/index.php\/2025\/11\/12\/2511-07604\/"},"modified":"2025-11-12T07:03:15","modified_gmt":"2025-11-12T07:03:15","slug":"2511-07604","status":"publish","type":"post","link":"https:\/\/mailitics.com\/index.php\/2025\/11\/12\/2511-07604\/","title":{"rendered":"Infinite-Dimensional Operator\/Block Kaczmarz Algorithms: Regret Bounds and $lambda$-Effectiveness"},"content":{"rendered":"

Infinite-Dimensional Operator\/Block Kaczmarz Algorithms: Regret Bounds and $lambda$-Effectiveness
\n \t

\n
<\/BR>
\n
\n \t

\n
<\/BR><\/p>\n

arXiv:2511.07604v1 Announce Type: new
\nAbstract: We present a variety of projection-based linear regression algorithms with a focus on modern machine-learning models and their algorithmic performance. We study the role of the relaxation parameter in generalized Kaczmarz algorithms and establish a priori regret bounds with explicit $lambda$-dependence to quantify how much an algorithm’s performance deviates from its optimal performance. A detailed analysis of relaxation parameter is also provided. Applications include: explicit regret bounds for the framework of Kaczmarz algorithm models, non-orthogonal Fourier expansions, and the use of regret estimates in modern machine learning models, including for noisy data, i.e., regret bounds for the noisy Kaczmarz algorithms. Motivated by machine-learning practice, our wider framework treats bounded operators (on infinite-dimensional Hilbert spaces), with updates realized as (block) Kaczmarz algorithms, leading to new and versatile results.<\/div>\n

\t

\n
<\/BR>
\n Halyun Jeong, Palle E. T. Jorgensen, Hyun-Kyoung Kwon, Myung-Sin Song
\n \t

\n
<\/BR>
\nGo to original source<\/a>
\n \t

\n
<\/BR><\/p>\n","protected":false},"excerpt":{"rendered":"

Infinite-Dimensional Operator\/Block Kaczmarz Algorithms: Regret Bounds and $lambda$-Effectiveness arXiv:2511.07604v1 Announce Type: new Abstract: We present a variety of projection-based linear regression algorithms with a focus on modern machine-learning models and their algorithmic performance. We study the role of the relaxation parameter in generalized Kaczmarz algorithms and establish a priori regret bounds with explicit $lambda$-dependence to […]<\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[62,113,1172,112],"tags":[821,2111,660],"class_list":["post-8302","post","type-post","status-publish","format-standard","hentry","category-aimldsaimlds","category-cs-lg","category-math-fa","category-stat-ml","tag-algorithms","tag-kaczmarz","tag-regret"],"_links":{"self":[{"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/posts\/8302"}],"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=8302"}],"version-history":[{"count":0,"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/posts\/8302\/revisions"}],"wp:attachment":[{"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/media?parent=8302"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/categories?post=8302"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/tags?post=8302"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}