Model Selection in Contextual Stochastic Bandit Problems


We study model selection in stochastic bandit problems. Our approach relies on a master algorithm that selects its actions among candidate base algorithms. While this problem is studied for specific classes of stochastic base algorithms, our objective is to provide a method that can work with more general classes of stochastic base algorithms. We propose a master algorithm inspired by CORRAL \cite{DBLP:conf/colt/AgarwalLNS17} and introduce a novel and generic smoothing transformation for stochastic bandit algorithms that permits us to obtain O(T‾‾√) regret guarantees for a wide class of base algorithms when working along with our master. We exhibit a lower bound showing that even when one of the base algorithms has O(logT) regret, in general it is impossible to get better than Ω(T‾‾√) regret in model selection, even asymptotically. We apply our algorithm to choose among different values of ϵ for the ϵ-greedy algorithm, and to choose between the k-armed UCB and linear UCB algorithms. Our empirical studies further confirm the effectiveness of our model-selection method.