{"id":2218,"date":"2025-03-05T07:04:46","date_gmt":"2025-03-05T07:04:46","guid":{"rendered":"https:\/\/mailitics.com\/index.php\/2025\/03\/05\/2503-02131\/"},"modified":"2025-03-05T07:04:46","modified_gmt":"2025-03-05T07:04:46","slug":"2503-02131","status":"publish","type":"post","link":"https:\/\/mailitics.com\/index.php\/2025\/03\/05\/2503-02131\/","title":{"rendered":"Gradient-free stochastic optimization for additive models"},"content":{"rendered":"

Gradient-free stochastic optimization for additive models
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arXiv:2503.02131v1 Announce Type: new
\nAbstract: We address the problem of zero-order optimization from noisy observations for an objective function satisfying the Polyak-{L}ojasiewicz or the strong convexity condition. Additionally, we assume that the objective function has an additive structure and satisfies a higher-order smoothness property, characterized by the H”older family of functions. The additive model for H”older classes of functions is well-studied in the literature on nonparametric function estimation, where it is shown that such a model benefits from a substantial improvement of the estimation accuracy compared to the H”older model without additive structure. We study this established framework in the context of gradient-free optimization. We propose a randomized gradient estimator that, when plugged into a gradient descent algorithm, allows one to achieve minimax optimal optimization error of the order $dT^{-(beta-1)\/beta}$, where $d$ is the dimension of the problem, $T$ is the number of queries and $betage 2$ is the H”older degree of smoothness. We conclude that, in contrast to nonparametric estimation problems, no substantial gain of accuracy can be achieved when using additive models in gradient-free optimization.<\/div>\n

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\n Arya Akhavan, Alexandre B. Tsybakov
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Gradient-free stochastic optimization for additive models arXiv:2503.02131v1 Announce Type: new Abstract: We address the problem of zero-order optimization from noisy observations for an objective function satisfying the Polyak-{L}ojasiewicz or the strong convexity condition. Additionally, we assume that the objective function has an additive structure and satisfies a higher-order smoothness property, characterized by the H”older family […]<\/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":[1387,379,483],"class_list":["post-2218","post","type-post","status-publish","format-standard","hentry","category-aimldsaimlds","category-cs-lg","category-stat-ml","tag-additive","tag-gradient","tag-optimization"],"_links":{"self":[{"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/posts\/2218"}],"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=2218"}],"version-history":[{"count":0,"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/posts\/2218\/revisions"}],"wp:attachment":[{"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/media?parent=2218"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/categories?post=2218"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/tags?post=2218"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}