Risk and Optimal Policies in Bandit Experiments.
We provide a decision‐theoretic 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 characte...
| Publicado en: | Econometrica Vol. 93; no. 3; pp. 1003 - 1030 |
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| Formato: | Artículo |
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Wiley-Blackwell
May2025
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| Acceso en línea: | Ver este registro en EBSCOhost |
| fields | @attributes: recordID: 1 pdfLink: plink: https://search.ebscohost.com/login.aspx?direct=true&db=ssf&AN=185839955&site=ehost-live header: @attributes: shortDbName: ssf uiTerm: 185839955 longDbName: Social Sciences Full Text (H.W. Wilson) uiTag: AN controlInfo: bkinfo: jinfo: jid: 00129682 ECN jtl: Econometrica issn: 00129682 maglogo: Y pubinfo: dt: May2025 vid: 93 iid: 3 pid: 480 pub: Wiley-Blackwell artinfo: ui: 185839955 10.3982/ECTA21075 ppf: 1003 ppct: 27 formats: tig: atl: Risk and Optimal Policies in Bandit Experiments. aug: au: Adusumilli, Karun affil: Department of Economics, University of Pennsylvania su: Decision making Decision theory Multi-armed bandit problem (Probability theory) Bayes' theorem Partial differential equations Feature selection Asymptotic expansions sug: subj: Decision making Decision theory Multi-armed bandit problem (Probability theory) Bayes' theorem Partial differential equations Feature selection Asymptotic expansions keyword: Bayes and minimax regret diffusion processes Multi‐armed bandits statistical decision theory Bayes and minimax regret diffusion processes Multi‐armed bandits statistical decision theory ab: We provide a decision‐theoretic 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‐order partial differential equation (PDE). Using a limit of experiments approach, we show that this PDE characterization also holds asymptotically under both parametric and non‐parametric 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. pubtype: Academic Journal doctype: Article src: R language: English refInfo: copyright: @attributes: flag: N holdings: @attributes: islocal: N |
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