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...
| Main Authors: | , |
|---|---|
| Formato: | Journal article |
| Idioma: | English |
| Publicado em: |
Institute of Mathematical Statistics and Bernoulli Society
2022
|
| Resumo: | 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. |
|---|