  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.
