{"data":{"id":"10.13016/m2ps3x","type":"dois","attributes":{"doi":"10.13016/m2ps3x","prefix":"10.13016","suffix":"m2ps3x","identifiers":[],"alternateIdentifiers":[],"creators":[{"name":"Ding, Zi","nameType":"Personal","givenName":"Zi","familyName":"Ding","affiliation":[],"nameIdentifiers":[]}],"titles":[{"title":"Optimal Learning with Non-Gaussian Rewards"}],"publisher":"Digital Repository at the University of Maryland","container":{},"publicationYear":2014,"subjects":[{"subject":"Mathematics","subjectScheme":"pqcontrolled"},{"subject":"FOS: Mathematics","schemeUri":"http://www.oecd.org/science/inno/38235147.pdf","subjectScheme":"Fields of Science and Technology (FOS)"},{"subject":"Operations research","subjectScheme":"pqcontrolled"},{"subject":"Bayesian learning","subjectScheme":"pquncontrolled"},{"subject":"Gittins Index","subjectScheme":"pquncontrolled"},{"subject":"non-Gaussian rewards","subjectScheme":"pquncontrolled"},{"subject":"Optimal learning","subjectScheme":"pquncontrolled"}],"contributors":[],"dates":[{"date":"2014","dateType":"Issued"}],"language":"en","types":{"ris":"THES","bibtex":"phdthesis","citeproc":"thesis","schemaOrg":"Thesis","resourceType":"Dissertation","resourceTypeGeneral":"Collection"},"relatedIdentifiers":[],"relatedItems":[],"sizes":[],"formats":[],"version":null,"rightsList":[],"descriptions":[{"description":"In this disseration, the author studies sequential Bayesian learning problems modeled under non-Gaussian distributions. We focus on a class of problems called the multi-armed bandit problem, and studies its optimal learning strategy, the Gittins index policy. The Gittins index is computationally intractable and approxi- mation methods have been developed for Gaussian reward problems. We construct a novel theoretical and computational framework for the Gittins index under non- Gaussian rewards. By interpolating the rewards using continuous-time conditional Levy processes, we recast the optimal stopping problems that characterize Gittins indices into free-boundary partial integro-differential equations (PIDEs). We also provide additional structural properties and numerical illustrations on how our ap- proach can be used to approximate the Gittins index.","descriptionType":"Abstract"}],"geoLocations":[],"fundingReferences":[],"xml":"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","url":"http://hdl.handle.net/1903/15774","contentUrl":null,"metadataVersion":0,"schemaVersion":"http://datacite.org/schema/kernel-2.2","source":null,"isActive":true,"state":"findable","reason":null,"viewCount":0,"viewsOverTime":[],"downloadCount":0,"downloadsOverTime":[],"referenceCount":0,"citationCount":0,"citationsOverTime":[],"partCount":0,"partOfCount":0,"versionCount":0,"versionOfCount":0,"created":"2014-10-11T05:52:09.000Z","registered":"2014-10-11T05:52:10.000Z","published":"2014","updated":"2020-08-19T16:54:34.000Z"},"relationships":{"client":{"data":{"id":"umd.lib","type":"clients"}},"provider":{"data":{"id":"umd","type":"providers"}},"media":{"data":{"id":"10.13016/m2ps3x","type":"media"}},"references":{"data":[]},"citations":{"data":[]},"parts":{"data":[]},"partOf":{"data":[]},"versions":{"data":[]},"versionOf":{"data":[]}}}}