Abstract

We introduce the problem of model selection for contextual bandits, where a learner must adapt to the complexity of the optimal policy while balancing exploration and exploitation. Our main result is a new model selection guarantee for linear contextual bandits. We work in the stochastic realizable setting with a sequence of nested linear policy classes of dimension where the m* -th class contains the optimal policy, and we design an algorithm that achieves regret with no prior knowledge of the optimal dimension The algorithm also achieves regret which is optimal for This is the first model selection result for contextual bandits with non-vacuous regret for all values of and to the best of our knowledge is the first positive result of this type for any online learning setting with partial information. The core of the algorithm is a new estimator for the gap in the best loss achievable by two linear policy classes, which we show admits a convergence rate faster than the rate required to learn the parameters for either class.