Sequential Multi-Hypothesis Testing in Multi-Armed Bandit Problems: An Approach for Asymptotic Optimality

We consider a multi-hypothesis testing problem involving $K$ -armed bandit. Each arm’s signal follows distribution from vector exponential family. The actual parameters of the arms are unknown to decision maker. maker incurs delay cost for until and switching whenever he switches one arm another. His goal is minimise overall reached on true hypothesis. Of interest policies that satisfy given constraint probability false detection. This sequential making where gets only limited view state nature at each stage, but can control his by choosing observe stage. An information-theoretic lower bound total (expected time reliable plus cost) first identified, variation policy based generalised likelihood ratio statistic then studied. Due family assumption, processing stage simple; associated conjugate prior model enables easy updates posterior distribution. proposed policy, with suitable threshold stopping, shown Under continuous selection also be asymptotically optimal in terms among all