Universal and data-adaptive algorithms for model selection in linear contextual bandits

TL;DR

This paper introduces adaptive algorithms for model selection in linear contextual bandits, achieving optimal exploration without requiring feature diversity conditions and extending to nested models.

Contribution

The paper presents new data-adaptive algorithms for model selection in linear contextual bandits with guarantees independent of feature diversity, including a best-of-both-worlds method.

Findings

Achieves model selection with $ ilde{O}(d^{eta} T^{1-eta})$ regret bounds.

Removes the need for feature-diversity conditions.

Extends to nested linear models under certain assumptions.

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 $\mathcal{O}(d^{\alpha} T^{1- \alpha})$ 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.