Generalized Policy Elimination: an efficient algorithm for Nonparametric Contextual Bandits
Aurelien Bibaut, Antoine Chambaz, Mark Laan
Abstract
We propose the Generalized Policy Elimination (GPE) algorithm, an oracle-efficient contextual bandit (CB) algorithm inspired by the Policy Elimination algorithm of Dudik et al. [2011]. 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.
BibTeX
@InProceedings{pmlr-v124-bibaut20a,
title = {Generalized Policy Elimination: an efficient algorithm for Nonparametric Contextual Bandits},
author = {Bibaut, Aurelien and Chambaz, Antoine and van der Laan, Mark},
booktitle = {Proceedings of the 36th Conference on Uncertainty in Artificial Intelligence (UAI)},
pages = {1099--1108},
year = {2020},
editor = {Peters, Jonas and Sontag, David},
volume = {124},
series = {Proceedings of Machine Learning Research},
month = {03--06 Aug},
publisher = {PMLR},
pdf = {http://proceedings.mlr.press/v124/bibaut20a/bibaut20a.pdf},
url = {https://proceedings.mlr.press/v124/bibaut20a.html},
abstract = {We propose the Generalized Policy Elimination (GPE) algorithm, an oracle-efficient contextual bandit (CB) algorithm inspired by the Policy Elimination algorithm of Dudik et al. [2011]. 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.}
}