# Active multiple matrix completion with adaptive confidence sets

arXiv: https://arxiv.org/abs/2605.02458 · HTML: https://mlsanity.com/paper/2605.02458/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 6 of its 24 references that are in the map.
- First posted on arXiv 4 May 2026.

## Builds on (most cited first, 6 of 6)

- [Stochastic Rank-1 Bandits](https://mlsanity.com/paper/1608.03023/) (2016)
- [Provable Efficient Online Matrix Completion via Non-convex Stochastic Gradient Descent](https://mlsanity.com/paper/1605.08370/) (2016)
- [Bernoulli Rank-1 Bandits for Click Feedback](https://mlsanity.com/paper/1703.06513/) (2017)
- [Active Learning for Accurate Estimation of Linear Models](https://mlsanity.com/paper/1703.00579/) (2017)
- [Online Matrix Completion and Online Robust PCA](https://mlsanity.com/paper/1503.03525/) (2015)
- [Online Matrix Completion Through Nuclear Norm Regularisation](https://mlsanity.com/paper/1401.2451/) (2014)

## Abstract (arXiv)

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.