Spotlight
Model Selection for Contextual Bandits
Dylan Foster · Akshay Krishnamurthy · Haipeng Luo

Wed Dec 11th 04:20 -- 04:25 PM @ West Exhibition Hall B

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 $d1 < d2 < \ldots$, where the $m^\star$-th class contains the optimal policy, and we design an algorithm that achieves $\tilde{O}l(T^{2/3}d^{1/3}{m^\star})$ regret with no prior knowledge of the optimal dimension $d{m^\star}$. The algorithm also achieves regret $\tilde{O}(T^{3/4} + \sqrt{Td{m^\star}})$, which is optimal for $d{m^{\star}}\geq{}\sqrt{T}$. This is the first model selection result for contextual bandits with non-vacuous regret for all values of $d_{m^\star}$, 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.

Author Information

Dylan Foster (MIT)
Akshay Krishnamurthy (Microsoft)
Haipeng Luo (University of Southern California)

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