Universal and data-adaptive algorithms for model selection in linear contextual bandits
Vidya K Muthukumar, Akshay Krishnamurthy
Abstract
Model selection in contextual bandits is an important complementary problem to regret minimization with respect to a fixed model class. We consider the simplest non-trivial instance of model-selection: distinguishing a simple multi-armed bandit problem from a linear contextual bandit problem. Even in this instance, current state-of-the-art methods explore in a suboptimal manner and require strong "feature-diversity" conditions. In this paper, we introduce new algorithms that a) explore in a data-adaptive manner, and b) provide model selection guarantees of the form O(d^{\alpha} T^{1 - \alpha}) with no feature diversity conditions whatsoever, where d denotes the dimension of the linear model and T denotes the total number of rounds. The first algorithm enjoys a "best-of-both-worlds" property, recovering two prior results that hold under distinct distributional assumptions, simultaneously. The second removes distributional assumptions altogether, expanding the scope for tractable model selection. Our approach extends to model selection among nested linear contextual bandits under some additional assumptions.
BibTeX
@InProceedings{pmlr-v162-muthukumar22a,
title = {Universal and data-adaptive algorithms for model selection in linear contextual bandits},
author = {Muthukumar, Vidya K and Krishnamurthy, Akshay},
booktitle = {Proceedings of the 39th International Conference on Machine Learning},
pages = {16197--16222},
year = {2022},
editor = {Chaudhuri, Kamalika and Jegelka, Stefanie and Song, Le and Szepesvari, Csaba and Niu, Gang and Sabato, Sivan},
volume = {162},
series = {Proceedings of Machine Learning Research},
month = {17--23 Jul},
publisher = {PMLR},
pdf = {https://proceedings.mlr.press/v162/muthukumar22a/muthukumar22a.pdf},
url = {https://proceedings.mlr.press/v162/muthukumar22a.html},
abstract = {Model selection in contextual bandits is an important complementary problem to regret minimization with respect to a fixed model class. We consider the simplest non-trivial instance of model-selection: distinguishing a simple multi-armed bandit problem from a linear contextual bandit problem. Even in this instance, current state-of-the-art methods explore in a suboptimal manner and require strong "feature-diversity" conditions. In this paper, we introduce new algorithms that a) explore in a data-adaptive manner, and b) provide model selection guarantees of the form O(d^{\alpha} T^{1 - \alpha}) with no feature diversity conditions whatsoever, where d denotes the dimension of the linear model and T denotes the total number of rounds. The first algorithm enjoys a "best-of-both-worlds" property, recovering two prior results that hold under distinct distributional assumptions, simultaneously. The second removes distributional assumptions altogether, expanding the scope for tractable model selection. Our approach extends to model selection among nested linear contextual bandits under some additional assumptions.}
}