Indexed Minimum Empirical Divergence for Unimodal Bandits

We consider a multi-armed bandit problem specified by a set of one-dimensional family exponential distributions endowed with a unimodal structure. We introduce IMED-UB, an algorithm that optimally exploits the unimodal-structure, by adapting to this setting the Indexed Minimum Empirical Divergence (IMED) algorithm introduced by Honda and Takemura [2015]. Owing to our proof technique, we are able to provide a concise finite-time analysis of the IMED-UBalgorithm. Numerical experiments show that IMED-UBcompetes with the state-of-the-art algorithms.