Generalized Policy Elimination: an efficient algorithm for Nonparametric Contextual Bandits
This work addresses the challenge of efficient learning in contextual bandits with complex, nonparametric policy classes, representing an incremental improvement over prior methods by extending regret guarantees to infinite-dimensional settings.
The authors tackled the problem of designing an efficient algorithm for nonparametric contextual bandits with infinite VC-dimension, resulting in the Generalized Policy Elimination (GPE) algorithm that achieves regret optimality up to logarithmic factors for policy classes with integrable entropy.
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.