Gittins' theorem under uncertainty
We study dynamic allocation problems for discrete time multi-armed bandits under uncertainty, based on the the theory of nonlinear expectations. We show that, under independence assumption on the bandits and with some relaxation in the definition of optimality, a Gittins allocation index gives optim...
| Hlavní autoři: | , |
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| Médium: | Journal article |
| Jazyk: | English |
| Vydáno: |
Institute of Mathematical Statistics and Bernoulli Society
2022
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| _version_ | 1826294388704149504 |
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| author | Cohen, SN Treetanthiploet, T |
| author_facet | Cohen, SN Treetanthiploet, T |
| author_sort | Cohen, SN |
| collection | OXFORD |
| description | We study dynamic allocation problems for discrete time multi-armed bandits under uncertainty, based on the the theory of nonlinear expectations. We show that, under independence assumption on the bandits and with some relaxation in the definition of optimality, a Gittins allocation index gives optimal choices. This involves studying the interaction of our uncertainty with controls which determine the filtration. We also run a simple numerical example which illustrates the interaction between the willingness to explore and uncertainty aversion of the agent when making decisions. |
| first_indexed | 2024-03-07T03:44:52Z |
| format | Journal article |
| id | oxford-uuid:bf200b78-bb8e-410b-924d-fdccf3898a49 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-07T03:44:52Z |
| publishDate | 2022 |
| publisher | Institute of Mathematical Statistics and Bernoulli Society |
| record_format | dspace |
| spelling | oxford-uuid:bf200b78-bb8e-410b-924d-fdccf3898a492022-03-27T05:45:04ZGittins' theorem under uncertaintyJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:bf200b78-bb8e-410b-924d-fdccf3898a49EnglishSymplectic ElementsInstitute of Mathematical Statistics and Bernoulli Society2022Cohen, SNTreetanthiploet, TWe study dynamic allocation problems for discrete time multi-armed bandits under uncertainty, based on the the theory of nonlinear expectations. We show that, under independence assumption on the bandits and with some relaxation in the definition of optimality, a Gittins allocation index gives optimal choices. This involves studying the interaction of our uncertainty with controls which determine the filtration. We also run a simple numerical example which illustrates the interaction between the willingness to explore and uncertainty aversion of the agent when making decisions. |
| spellingShingle | Cohen, SN Treetanthiploet, T Gittins' theorem under uncertainty |
| title | Gittins' theorem under uncertainty |
| title_full | Gittins' theorem under uncertainty |
| title_fullStr | Gittins' theorem under uncertainty |
| title_full_unstemmed | Gittins' theorem under uncertainty |
| title_short | Gittins' theorem under uncertainty |
| title_sort | gittins theorem under uncertainty |
| work_keys_str_mv | AT cohensn gittinstheoremunderuncertainty AT treetanthiploett gittinstheoremunderuncertainty |