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Sci. Comput."],"published-print":{"date-parts":[[2022,2]]},"abstract":"<jats:p>Multifidelity approximation is an important technique in scientific computation and simulation. In this paper, we introduce a bandit-learning approach for leveraging data of varying fidelities to achieve precise estimates of the parameters of interest. Under a linear model assumption, we formulate a multifidelity approximation as a modified stochastic bandit and analyze the loss for a class of policies that uniformly explore each model before exploiting. Utilizing the estimated conditional mean-squared error, we propose a consistent algorithm, adaptive explore-then-commit (AETC), and establish a corresponding trajectorywise optimality result. These results are then extended to the case of vector-valued responses, where we demonstrate that the algorithm is efficient without the need to worry about estimating high-dimensional parameters. The main advantage of our approach is that we require neither hierarchical model structure nor a priori knowledge of statistical information (e.g., correlations) about or between models. Instead, the AETC algorithm requires only knowledge of which model is a trusted high-fidelity model, along with (relative) computational cost estimates of querying each model. Numerical experiments are provided at the end to support our theoretical findings.<\/jats:p>","DOI":"10.1137\/21m1408312","type":"journal-article","created":{"date-parts":[[2022,1,18]],"date-time":"2022-01-18T11:20:18Z","timestamp":1642504818000},"page":"A150-A175","source":"Crossref","is-referenced-by-count":8,"title":["A Bandit-Learning Approach to Multifidelity Approximation"],"prefix":"10.1137","volume":"44","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-7223-8147","authenticated-orcid":true,"given":"Yiming","family":"Xu","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Vahid","family":"Keshavarzzadeh","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Robert M.","family":"Kirby","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5914-4207","authenticated-orcid":true,"given":"Akil","family":"Narayan","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2022,1,18]]},"reference":[{"key":"atypb1","doi-asserted-by":"publisher","DOI":"10.1007\/BF01197433"},{"key":"atypb2","doi-asserted-by":"publisher","DOI":"10.2514\/2.2877"},{"key":"atypb3","doi-asserted-by":"publisher","DOI":"10.1109\/TAC.1987.1104485"},{"key":"atypb4","first-page":"41","volume-title":"Proceedings of COLT","author":"Audibert J.-Y.","year":"2010"},{"key":"atypb5","doi-asserted-by":"publisher","DOI":"10.1023\/A:1013689704352"},{"key":"atypb6","doi-asserted-by":"publisher","DOI":"10.1109\/SFCS.1995.492488"},{"key":"atypb7","doi-asserted-by":"publisher","DOI":"10.1137\/S0097539701398375"},{"key":"atypb8","doi-asserted-by":"publisher","DOI":"10.1007\/s10998-010-3055-6"},{"key":"atypb9","doi-asserted-by":"publisher","DOI":"10.1137\/130932715"},{"key":"atypb10","doi-asserted-by":"publisher","DOI":"10.1109\/CEC48606.2020.9185782"},{"key":"atypb11","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4419-8724-2"},{"key":"atypb12","doi-asserted-by":"publisher","DOI":"10.1561\/2200000024"},{"key":"atypb13","volume-title":"Conference on Learning Theory, JMLR Workshop and Conference Proceedings","author":"Bubeck S.","year":"2012"},{"key":"atypb14","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-04414-4_7"},{"key":"atypb15","doi-asserted-by":"publisher","DOI":"10.1145\/1961189.1961199"},{"key":"atypb16","doi-asserted-by":"publisher","DOI":"10.1198\/106186005X76983"},{"key":"atypb17","doi-asserted-by":"publisher","DOI":"10.1023\/A:1022627411411"},{"key":"atypb18","volume-title":"Proceedings of the 21st Annual Conference on Learning Theory","author":"Dani V.","year":"2008"},{"key":"atypb19","doi-asserted-by":"publisher","DOI":"10.2514\/6.2004-4457"},{"key":"atypb20","doi-asserted-by":"publisher","DOI":"10.1016\/j.paerosci.2008.11.001"},{"key":"atypb21","doi-asserted-by":"publisher","DOI":"10.1002\/9780470770801"},{"key":"atypb22","first-page":"91","volume-title":"Proceedings of The Art and Science of Bayesian Image Analysis","author":"Fox C.","year":"1997"},{"key":"atypb23","first-page":"998","volume-title":"Proceedings of the Conference on Learning Theory, PMLR","author":"Garivier A.","year":"2016"},{"key":"atypb24","doi-asserted-by":"publisher","DOI":"10.1287\/opre.1070.0496"},{"key":"atypb25","doi-asserted-by":"publisher","DOI":"10.1017\/S096249291500001X"},{"key":"atypb26","doi-asserted-by":"crossref","first-page":"148","DOI":"10.1111\/j.2517-6161.1979.tb01068.x","volume":"41","author":"Gittins J. 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