Reviews: Personalizing Many Decisions with High-Dimensional Covariates

Summary: This paper studies the problem of regret minimization for low-rank linear contextual bandits. In the setting considered, there are k arms, each with an unknown d dimensional vector where k and d are assumed to be large. However, the k by d matrix of arms' feature vectors is assumed to be low rank with rank r, making some amount of information sharing for estimating different arms possible. At each time step, the algorithm proceeds as follows. First, a context is drawn iid from a distribution, similar to existing work.