Active multiple matrix completion with adaptive confidence sets
This work addresses the challenge of active learning for multiple matrix completion problems with unknown ranks, relevant for applications like market segmentation.
The paper introduces a multi-task active learning setting for matrix completion, where the learner selects which matrix to sample from at each round. The proposed algorithm MAlocate adapts to unknown matrix ranks and is proven minimax-optimal, with synthetic experiments demonstrating its performance.
In this work, we formulate a new multi-task active learning setting in which the learner's goal is to solve multiple matrix completion problems simultaneously. At each round, the learner can choose from which matrix it receives a sample from an entry drawn uniformly at random. Our main practical motivation is market segmentation, where the matrices represent 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 which is unknown. We provide and analyze a new algorithm, MAlocate that is able to adapt to the unknown ranks of the different matrices. We then give a lower-bound showing that our strategy is minimax-optimal and demonstrate its performance with synthetic experiments.