Active multiple matrix completion with adaptive confidence sets

We address the problem of an active setting for a matrix completion, where the learner can choose, from which matrix, it receives a sample (drawn uniformly at random). Our main practical motivation is the market segmentation, where the matrices are different regions with different preferences of the customers. The challenge in this setting is that each of the matrices can be of a different size and also of a different rank. We provide and analyze a new algorithm, MAlocate that is able to adapt to the ranks of the different matrices. We also prove a lower-bound showing that our strategy is minimax-optimal, and we demonstrate its performance with synthetic experiments.