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We focus upon developing an unbiased method via the underdamped Langevin dynamics, which has proven to be popular of late due to applications in statistics and machine learning. Specifically in continuous time, the dynamics can be constructed to admit the probability of interest as a stationary measure. We develop a novel scheme based upon doubly randomized estimation as in [J. Heng, J. Houssineau, and A. Jasra, On Unbiased Score Estimation for Partially Observed Diffusions, preprint, 2021] and [J. Heng, A. Jasra, K. J. H. Law, and A. Tarakanov, SIAM\/ASA J. Uncertain. Quantif., 11 (2023), pp. 616\u2013645], which requires access only to time-discretized versions of the dynamics, i.e., the ones used in practical algorithms. We prove, under standard assumptions, that our estimator is of finite variance and either has finite expected cost or has finite cost with a high probability. To illustrate our theoretical findings we provide numerical experiments that verify our theory, which include challenging examples from Bayesian statistics and statistical physics.<\/jats:p>","DOI":"10.1137\/22m1503385","type":"journal-article","created":{"date-parts":[[2023,12,5]],"date-time":"2023-12-05T04:51:30Z","timestamp":1701751890000},"page":"A3047-A3070","source":"Crossref","is-referenced-by-count":7,"title":["Unbiased Estimation Using Underdamped Langevin Dynamics"],"prefix":"10.1137","volume":"45","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-6394-0695","authenticated-orcid":true,"given":"Hamza","family":"Ruzayqat","sequence":"first","affiliation":[{"name":"Computer, Electrical, and Mathematical Sciences and Engineering Division, King Abdullah University of Science and Technology, Thuwal, 23955, Kingdom of Saudi Arabia."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Neil K.","family":"Chada","sequence":"additional","affiliation":[{"name":"Department of Actuarial Mathematics and Statistics, Heriot Watt University, Edinburgh, EH14 4AS, UK."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4808-9131","authenticated-orcid":true,"given":"Ajay","family":"Jasra","sequence":"additional","affiliation":[{"name":"Computer, Electrical, and Mathematical Sciences and Engineering Division, King Abdullah University of Science and Technology, Thuwal, 23955, Kingdom of Saudi Arabia."}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2023,12,5]]},"reference":[{"key":"ref1","volume-title":"Applications of Mathematics","author":"Benveniste A.","year":"1990"},{"key":"ref2","doi-asserted-by":"publisher","DOI":"10.1111\/j.1467-9868.2006.00552.x"},{"key":"ref3","doi-asserted-by":"publisher","DOI":"10.1214\/105051605000000485"},{"key":"ref4","doi-asserted-by":"publisher","DOI":"10.1214\/19-AAP1528"},{"key":"ref5","doi-asserted-by":"publisher","DOI":"10.1137\/20M131549X"},{"key":"ref6","first-page":"20210710","volume":"478","author":"Chada N. 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