Regret bounds for meta Bayesian optimization with an unknown Gaussian process prior
© 2018 Curran Associates Inc.All rights reserved. Bayesian optimization usually assumes that a Bayesian prior is given. However, the strong theoretical guarantees in Bayesian optimization are often regrettably compromised in practice because of unknown parameters in the prior. In this paper, we adop...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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2021
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| Online Access: | https://hdl.handle.net/1721.1/137709 |
| _version_ | 1811094567957561344 |
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| author | Kaelbling, Leslie P. Kim, Beomjoon Wang, Zi |
| author_facet | Kaelbling, Leslie P. Kim, Beomjoon Wang, Zi |
| author_sort | Kaelbling, Leslie P. |
| collection | MIT |
| description | © 2018 Curran Associates Inc.All rights reserved. Bayesian optimization usually assumes that a Bayesian prior is given. However, the strong theoretical guarantees in Bayesian optimization are often regrettably compromised in practice because of unknown parameters in the prior. In this paper, we adopt a variant of empirical Bayes and show that, by estimating the Gaussian process prior from offline data sampled from the same prior and constructing unbiased estimators of the posterior, variants of both GP-UCB and probability of improvement achieve a near-zero regret bound, which decreases to a constant proportional to the observational noise as the number of offline data and the number of online evaluations increase. Empirically, we have verified our approach on challenging simulated robotic problems featuring task and motion planning. |
| first_indexed | 2024-09-23T16:02:08Z |
| format | Article |
| id | mit-1721.1/137709 |
| institution | Massachusetts Institute of Technology |
| language | English |
| last_indexed | 2024-09-23T16:02:08Z |
| publishDate | 2021 |
| record_format | dspace |
| spelling | mit-1721.1/1377092021-11-09T03:03:14Z Regret bounds for meta Bayesian optimization with an unknown Gaussian process prior Kaelbling, Leslie P. Kim, Beomjoon Wang, Zi © 2018 Curran Associates Inc.All rights reserved. Bayesian optimization usually assumes that a Bayesian prior is given. However, the strong theoretical guarantees in Bayesian optimization are often regrettably compromised in practice because of unknown parameters in the prior. In this paper, we adopt a variant of empirical Bayes and show that, by estimating the Gaussian process prior from offline data sampled from the same prior and constructing unbiased estimators of the posterior, variants of both GP-UCB and probability of improvement achieve a near-zero regret bound, which decreases to a constant proportional to the observational noise as the number of offline data and the number of online evaluations increase. Empirically, we have verified our approach on challenging simulated robotic problems featuring task and motion planning. 2021-11-08T16:52:46Z 2021-11-08T16:52:46Z 2018 2019-06-04T15:32:47Z Article http://purl.org/eprint/type/ConferencePaper https://hdl.handle.net/1721.1/137709 Kaelbling, Leslie P., Kim, Beomjoon and Wang, Zi. 2018. "Regret bounds for meta Bayesian optimization with an unknown Gaussian process prior." en https://papers.nips.cc/paper/2018 Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use. application/pdf Neural Information Processing Systems (NIPS) |
| spellingShingle | Kaelbling, Leslie P. Kim, Beomjoon Wang, Zi Regret bounds for meta Bayesian optimization with an unknown Gaussian process prior |
| title | Regret bounds for meta Bayesian optimization with an unknown Gaussian process prior |
| title_full | Regret bounds for meta Bayesian optimization with an unknown Gaussian process prior |
| title_fullStr | Regret bounds for meta Bayesian optimization with an unknown Gaussian process prior |
| title_full_unstemmed | Regret bounds for meta Bayesian optimization with an unknown Gaussian process prior |
| title_short | Regret bounds for meta Bayesian optimization with an unknown Gaussian process prior |
| title_sort | regret bounds for meta bayesian optimization with an unknown gaussian process prior |
| url | https://hdl.handle.net/1721.1/137709 |
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