{"id":4960,"date":"2025-06-30T07:02:25","date_gmt":"2025-06-30T07:02:25","guid":{"rendered":"https:\/\/mailitics.com\/index.php\/2025\/06\/30\/2506-21894\/"},"modified":"2025-06-30T07:02:25","modified_gmt":"2025-06-30T07:02:25","slug":"2506-21894","status":"publish","type":"post","link":"https:\/\/mailitics.com\/index.php\/2025\/06\/30\/2506-21894\/","title":{"rendered":"Thompson Sampling in Function Spaces via Neural Operators"},"content":{"rendered":"

Thompson Sampling in Function Spaces via Neural Operators
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arXiv:2506.21894v1 Announce Type: new
\nAbstract: We propose an extension of Thompson sampling to optimization problems over function spaces where the objective is a known functional of an unknown operator’s output. We assume that functional evaluations are inexpensive, while queries to the operator (such as running a high-fidelity simulator) are costly. Our algorithm employs a sample-then-optimize approach using neural operator surrogates. This strategy avoids explicit uncertainty quantification by treating trained neural operators as approximate samples from a Gaussian process. We provide novel theoretical convergence guarantees, based on Gaussian processes in the infinite-dimensional setting, under minimal assumptions. We benchmark our method against existing baselines on functional optimization tasks involving partial differential equations and other nonlinear operator-driven phenomena, demonstrating improved sample efficiency and competitive performance.<\/div>\n

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\n Rafael Oliveira, Xuesong Wang, Kian Ming A. Chai, Edwin V. Bonilla
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Thompson Sampling in Function Spaces via Neural Operators arXiv:2506.21894v1 Announce Type: new Abstract: We propose an extension of Thompson sampling to optimization problems over function spaces where the objective is a known functional of an unknown operator’s output. We assume that functional evaluations are inexpensive, while queries to the operator (such as running a high-fidelity […]<\/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":[118,1529,124],"class_list":["post-4960","post","type-post","status-publish","format-standard","hentry","category-aimldsaimlds","category-cs-lg","category-stat-ml","tag-neural","tag-operator","tag-thompson"],"_links":{"self":[{"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/posts\/4960"}],"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=4960"}],"version-history":[{"count":0,"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/posts\/4960\/revisions"}],"wp:attachment":[{"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/media?parent=4960"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/categories?post=4960"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/tags?post=4960"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}