Towards Costless Model Selection in Contextual Bandits: A Bias-Variance Perspective

TL;DR

This paper explores conditions under which costless model selection in stochastic contextual bandits is possible, introducing a novel algorithm that adapts to the evolving bias-variance trade-off for improved regret guarantees.

Contribution

It identifies benign conditions enabling costless model selection in contextual bandits and proposes a new adaptive algorithm based on a misspecification test.

Findings

The algorithm adapts to the complexity of the simplest class with dominant estimation variance.

Under certain conditions, it guarantees improved regret bounds for short horizons.

The approach demonstrates benefits of model selection in reward estimation for contextual bandits.

Abstract

Model selection in supervised learning provides costless guarantees as if the model that best balances bias and variance was known a priori. We study the feasibility of similar guarantees for cumulative regret minimization in the stochastic contextual bandit setting. Recent work [Marinov and Zimmert, 2021] identifies instances where no algorithm can guarantee costless regret bounds. Nevertheless, we identify benign conditions where costless model selection is feasible: gradually increasing class complexity, and diminishing marginal returns for best-in-class policy value with increasing class complexity. Our algorithm is based on a novel misspecification test, and our analysis demonstrates the benefits of using model selection for reward estimation. Unlike prior work on model selection in contextual bandits, our algorithm carefully adapts to the evolving bias-variance trade-off as more data is collected. In particular, our algorithm and analysis go beyond adapting to the complexity of the simplest realizable class and instead adapt to the complexity of the simplest class whose estimation variance dominates the bias. For short horizons, this provides improved regret guarantees that depend on the complexity of simpler classes.