Abstract : We study the problem of minimising regret in two-armed bandit problems with Gaussian rewards. Our objective is to use this simple setting to illustrate that strategies based on an exploration phase (up to a stopping time) followed by exploitation are necessarily suboptimal. The results hold regardless of whether or not the difference in means between the two arms is known. Besides the main message, we also refine existing deviation inequalities, which allow us to design fully sequential strategies with finite-time regret guarantees that are (a) asymptotically optimal as the horizon grows and (b) order-optimal in the minimax sense. Furthermore we provide empirical evidence that the theory also holds in practice and discuss extensions to non-gaussian and multiple-armed case.
https://hal.archives-ouvertes.fr/hal-01322906
Contributor : Emilie Kaufmann
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Submitted on : Monday, November 14, 2016 - 1:19:04 PM
Last modification on : Friday, October 25, 2019 - 2:04:46 AM
Long-term archiving on: Tuesday, March 21, 2017 - 12:39:18 AM
