"We propose the Generalized Policy Elimination (GPE) algorithm, an
oracle-efficient contextual bandit (CB) algorithm inspired by the Policy
Elimination algorithm of \cite{dudik2011}. We prove the first
regret-optimality guarantee theorem for an oracle-efficient CB algorithm
competing against a nonparametric class with infinite VC-dimension.
Specifically, we show that GPE is regret-optimal (up to logarithmic factors)
for policy classes with integrable entropy.

For classes with larger entropy, we show that the core techniques used to
analyze GPE can be used to design an $\varepsilon$-greedy algorithm with
regret bound matching that of the best algorithms to date. We illustrate
the applicability of our algorithms and theorems with examples of large
nonparametric policy classes, for which the relevant optimization oracles
can be efficiently implemented."

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