{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T19:23:58Z","timestamp":1787340238291,"version":"3.56.0"},"reference-count":47,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"1","funder":[{"DOI":"10.13039\/100000121","name":"Division of Mathematical Sciences","doi-asserted-by":"publisher","award":["1222262"],"award-info":[{"award-number":["1222262"]}],"id":[{"id":"10.13039\/100000121","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM\/ASA J. Uncertainty Quantification"],"published-print":{"date-parts":[[2017,1]]},"abstract":"<jats:p>Motivated by the problem of estimating optimal feedback policy maps in stochastic control applications, we propose and analyze sequential design methods for ranking several response surfaces. Namely, given $L \\ge 2$ response surfaces over a continuous input space $\\mathcal{X}$, the aim is to efficiently find the index of the minimal response across the entire $\\mathcal{X}$. The response surfaces are not known and have to be noisily sampled one at a time, requiring joint experimental design both in space and response-index dimensions. To generate sequential design heuristics we investigate Bayesian stepwise uncertainty reduction approaches, as well as sampling based on posterior classification complexity. We also make connections between our continuous-input formulation and the discrete framework of pure regret in multi-armed bandits. To model the response surfaces we utilize kriging metamodels. Several numerical examples using both synthetic data and an epidemics control problem are provided to illustrate our approach and the efficacy of respective adaptive designs.<\/jats:p>","DOI":"10.1137\/15m1045168","type":"journal-article","created":{"date-parts":[[2017,2,28]],"date-time":"2017-02-28T11:19:31Z","timestamp":1488280771000},"page":"212-239","source":"Crossref","is-referenced-by-count":27,"title":["Sequential Design for Ranking Response Surfaces"],"prefix":"10.1137","volume":"5","author":[{"given":"Ruimeng","family":"Hu","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Mike","family":"Ludkovski","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2017,2,28]]},"reference":[{"key":"atypb1","doi-asserted-by":"publisher","DOI":"10.1137\/120897298"},{"key":"atypb2","doi-asserted-by":"crossref","unstructured":"R. Anderson and D. Milutinovic,\n                      A stochastic approach to Dubins feedback control for target tracking\n                      , in 2011 IEEE\/RSJ International Conference on Intelligent Robots and Systems, 2011, pp. 3917-3922.","DOI":"10.1109\/IROS.2011.6094760"},{"key":"atypb3","doi-asserted-by":"publisher","DOI":"10.1287\/opre.1090.0754"},{"key":"atypb4","doi-asserted-by":"publisher","DOI":"10.1023\/A:1013689704352"},{"key":"atypb5","first-page":"109","author":"Azimi J.","year":"2010","journal-title":"NY"},{"key":"atypb6","doi-asserted-by":"publisher","DOI":"10.1007\/s11222-011-9241-4"},{"key":"atypb7","doi-asserted-by":"publisher","DOI":"10.1016\/j.tcs.2010.12.059"},{"key":"atypb8","first-page":"1655","volume":"12","author":"Bubeck S.","year":"2011","journal-title":"J. Mach. Learn. 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Syst., ("},{"key":"atypb28","unstructured":"M. W. Hoffman, B. Shahriari, and N. de Freitas,\n                      Exploiting correlation and budget constraints in Bayesian multi-armed bandit optimization\n                      , tech. report, arXiv preprinthttps:\/\/arxiv.org\/abs\/1303.6746, 2013."},{"key":"atypb29","doi-asserted-by":"publisher","DOI":"10.1023\/A:1008306431147"},{"key":"atypb30","first-page":"2372","author":"Joshi A.","year":"2009","journal-title":"NJ"},{"key":"atypb31","doi-asserted-by":"publisher","DOI":"10.1287\/opre.1100.0909"},{"key":"atypb32","doi-asserted-by":"publisher","DOI":"10.1007\/s11222-013-9419-z"},{"key":"atypb33","doi-asserted-by":"publisher","DOI":"10.1093\/rfs\/14.1.113"},{"key":"atypb34","doi-asserted-by":"crossref","unstructured":"M. Ludkovski and J. 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