{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,23]],"date-time":"2026-09-23T15:44:14Z","timestamp":1790178254098,"version":"4.1.0"},"reference-count":31,"publisher":"The Econometric Society","issue":"3","license":[{"start":{"date-parts":[[2025,1,1]],"date-time":"2025-01-01T00:00:00Z","timestamp":1735689600000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by-nc\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["ECTA"],"abstract":"<jats:p>We provide a decision\u2010theoretic analysis of bandit experiments under local asymptotics. Working within the framework of diffusion processes, we define suitable notions of asymptotic Bayes and minimax risk for these experiments. For normally distributed rewards, the minimal Bayes risk can be characterized as the solution to a second\u2010order partial differential equation (PDE). Using a limit of experiments approach, we show that this PDE characterization also holds asymptotically under both parametric and non\u2010parametric distributions of the rewards. The approach further describes the state variables it is asymptotically sufficient to restrict attention to, and thereby suggests a practical strategy for dimension reduction. The PDEs characterizing minimal Bayes risk can be solved efficiently using sparse matrix routines or Monte Carlo methods. We derive the optimal Bayes and minimax policies from their numerical solutions. These optimal policies substantially dominate existing methods such as Thompson sampling; the risk of the latter is often twice as high.<\/jats:p>","DOI":"10.3982\/ecta21075","type":"journal-article","created":{"date-parts":[[2025,6,2]],"date-time":"2025-06-02T05:09:42Z","timestamp":1748840982000},"page":"1003-1029","source":"Crossref","is-referenced-by-count":4,"title":["Risk and Optimal Policies in Bandit Experiments"],"prefix":"10.3982","volume":"93","author":[{"given":"Karun","family":"Adusumilli","sequence":"first","affiliation":[{"name":"Department of Economics, University of Pennsylvania"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"2359","published-online":{"date-parts":[[2025]]},"reference":[{"key":"ecta200785-bib-0001","unstructured":"Adusumilli, Karun (2022a): \u201cHow to Sample and When to Stop Sampling: The Generalized Wald Problem and Minimax Policies,\u201d arXiv preprint arXiv:2210.15841."},{"key":"ecta200785-bib-0002","unstructured":"Adusumilli, Karun (2022b): \u201cMinimax Policies for Best Arm Identification With Two Arms,\u201d. arXiv preprint arXiv:2204.05527."},{"key":"ecta200785-bib-0003","doi-asserted-by":"crossref","unstructured":"Adusumilli, Karun (2025): \u201cSupplement to \u2018Risk and Optimal Policies in Bandit Experiments\u2019,\u201d Econometrica Supplemental Material, 93, https:\/\/doi.org\/10.3982\/ECTA21075.","DOI":"10.3982\/ECTA21075"},{"key":"ecta200785-bib-0004","unstructured":"Athey, Susan, Katy Bergstrom, Vitor Hadad, Julian C. 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