{"id":1693,"date":"2025-02-06T07:02:29","date_gmt":"2025-02-06T07:02:29","guid":{"rendered":"https:\/\/mailitics.com\/index.php\/2025\/02\/06\/2502-02859\/"},"modified":"2025-02-06T07:02:29","modified_gmt":"2025-02-06T07:02:29","slug":"2502-02859","status":"publish","type":"post","link":"https:\/\/mailitics.com\/index.php\/2025\/02\/06\/2502-02859\/","title":{"rendered":"Gap-Dependent Bounds for Federated $Q$-learning"},"content":{"rendered":"

Gap-Dependent Bounds for Federated $Q$-learning
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arXiv:2502.02859v1 Announce Type: new
\nAbstract: We present the first gap-dependent analysis of regret and communication cost for on-policy federated $Q$-Learning in tabular episodic finite-horizon Markov decision processes (MDPs). Existing FRL methods focus on worst-case scenarios, leading to $sqrt{T}$-type regret bounds and communication cost bounds with a $log T$ term scaling with the number of agents $M$, states $S$, and actions $A$, where $T$ is the average total number of steps per agent. In contrast, our novel framework leverages the benign structures of MDPs, such as a strictly positive suboptimality gap, to achieve a $log T$-type regret bound and a refined communication cost bound that disentangles exploration and exploitation. Our gap-dependent regret bound reveals a distinct multi-agent speedup pattern, and our gap-dependent communication cost bound removes the dependence on $MSA$ from the $log T$ term. Notably, our gap-dependent communication cost bound also yields a better global switching cost when $M=1$, removing $SA$ from the $log T$ term.<\/div>\n

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\n Haochen Zhang, Zhong Zheng, Lingzhou Xue
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Gap-Dependent Bounds for Federated $Q$-learning arXiv:2502.02859v1 Announce Type: new Abstract: We present the first gap-dependent analysis of regret and communication cost for on-policy federated $Q$-Learning in tabular episodic finite-horizon Markov decision processes (MDPs). Existing FRL methods focus on worst-case scenarios, leading to $sqrt{T}$-type regret bounds and communication cost bounds with a $log T$ term scaling […]<\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[62,113,112],"tags":[1659,1658,1657],"class_list":["post-1693","post","type-post","status-publish","format-standard","hentry","category-aimldsaimlds","category-cs-lg","category-stat-ml","tag-cost","tag-dependent","tag-gap"],"_links":{"self":[{"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/posts\/1693"}],"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=1693"}],"version-history":[{"count":0,"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/posts\/1693\/revisions"}],"wp:attachment":[{"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/media?parent=1693"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/categories?post=1693"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/tags?post=1693"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}