{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,18]],"date-time":"2026-08-18T01:20:50Z","timestamp":1787016050599,"version":"build-2736575974"},"reference-count":55,"publisher":"Oxford University Press (OUP)","issue":"1","license":[{"start":{"date-parts":[[2023,2,24]],"date-time":"2023-02-24T00:00:00Z","timestamp":1677196800000},"content-version":"vor","delay-in-days":807,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["IIS-1149662"],"award-info":[{"award-number":["IIS-1149662"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["IIS-1409177"],"award-info":[{"award-number":["IIS-1409177"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000006","name":"Office of Naval Research","doi-asserted-by":"publisher","award":["N00014-14-1-0485"],"award-info":[{"award-number":["N00014-14-1-0485"]}],"id":[{"id":"10.13039\/100000006","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000006","name":"Office of Naval Research","doi-asserted-by":"publisher","award":["N00014-17-1-2131"],"award-info":[{"award-number":["N00014-17-1-2131"]}],"id":[{"id":"10.13039\/100000006","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Shutzer Fellowship"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2021,2,1]]},"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>The need for statistical estimation with large data sets has reinvigorated interest in iterative procedures and stochastic optimization. Stochastic approximations are at the forefront of this recent development as they yield procedures that are simple, general and fast. However, standard stochastic approximations are often numerically unstable. Deterministic optimization, in contrast, increasingly uses proximal updates to achieve numerical stability in a principled manner. A theoretical gap has thus emerged. While standard stochastic approximations are subsumed by the framework Robbins and Monro (The annals of mathematical statistics, 1951, pp. 400\u2013407), there is no such framework for stochastic approximations with proximal updates. In this paper, we conceptualize a proximal version of the classical Robbins\u2013Monro procedure. Our theoretical analysis demonstrates that the proposed procedure has important stability benefits over the classical Robbins\u2013Monro procedure, while it retains the best known convergence rates. Exact implementations of the proximal Robbins\u2013Monro procedure are challenging, but we show that approximate implementations lead to procedures that are easy to implement, and still dominate standard procedures by achieving numerical stability, practically without trade-offs. Moreover, approximate proximal Robbins\u2013Monro procedures can be applied even when the objective cannot be calculated analytically, and so they generalize stochastic proximal procedures currently in use.<\/jats:p>","DOI":"10.1111\/rssb.12405","type":"journal-article","created":{"date-parts":[[2020,12,10]],"date-time":"2020-12-10T16:27:05Z","timestamp":1607617625000},"page":"188-212","source":"Crossref","is-referenced-by-count":16,"title":["The Proximal Robbins\u2013Monro Method"],"prefix":"10.1093","volume":"83","author":[{"given":"Panos","family":"Toulis","sequence":"first","affiliation":[{"name":"Booth School of Business \u00a0 , Chicago, IL , USA"},{"name":"University of Chicago \u00a0 , Chicago, IL , USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Thibaut","family":"Horel","sequence":"additional","affiliation":[{"name":"Department of Computer Science \u00a0 , Cambridge, MA , USA"},{"name":"Harvard University \u00a0 , Cambridge, MA , USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Edoardo M.","family":"Airoldi","sequence":"additional","affiliation":[{"name":"Fox School of Business \u00a0 , Philadelphia, PA , USA"},{"name":"Temple University \u00a0 , Philadelphia, PA , USA"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"286","published-online":{"date-parts":[[2020,12,9]]},"reference":[{"issue":"2","key":"2023022408365935500_","doi-asserted-by":"crossref","first-page":"251","DOI":"10.1162\/089976698300017746","article-title":"Natural gradient works efficiently in learning","volume":"10","author":"Amari","year":"1998","journal-title":"Neural Computation"},{"key":"2023022408365935500_","doi-asserted-by":"crossref","DOI":"10.1073\/pnas.1908018116","volume-title":"The importance of better models in stochastic optimization","author":"Asi","year":"2019"},{"key":"2023022408365935500_","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4419-9467-7","volume-title":"Convex analysis and 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