Semi-Parametric Batched Global Multi-Armed Bandits with Covariates

Music City Center 

In applications such as clinical trials, treatment decisions are usually made in phases/batches, where information from the previous batch is used to determine the treatments allocated in the upcoming batch. Such scenarios can naturally be seen to fall in the batched bandits framework. While batched bandit frameworks have been studied in parametric and nonparametric regression settings, we propose a novel semi-parametric bandit approach that promotes interpretability and dimension reduction in nonparametric batched bandits. We assume that the reward-covariate relationship can be modelled in a reduced 1-dimensional central subspace based on the single-index regression framework. We adopt an adaptive binning and successive elimination algorithm and provide optimal regret guarantees for the same. We also illustrate the performance of the algorithm on simulated and real datasets.

multi-armed bandits

semi-parametric

single-index regression

dynamic binning

successive elimination

regret bounds 

Section on Statistical Learning and Data Science