Papers › Model selection for contextual bandits
Model selection for contextual bandits
Dylan J. Foster, Akshay Krishnamurthy, Haipeng Luo
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 d₁ < d₂ < …, where the m^⋆-th class contains the optimal policy, and we design an algorithm that achieves Õ(T^(2/3)d^(1/3)_(m^⋆)) regret with no prior knowledge of the optimal dimension d_(m^⋆). The algorithm also achieves regret Õ(T^(3/4) + √(Td_(m^⋆))), which is optimal for d_(m^⋆)≥√(T). This is the first model selection result for contextual bandits with non-vacuous regret for all values of d_(m^⋆), 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.
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