Active multiple matrix completion with adaptive confidence sets
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866909011830374400 |
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| author | Locatelli, Andrea Carpentier, Alexandra Valko, Michal |
| author_facet | Locatelli, Andrea Carpentier, Alexandra Valko, Michal |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_02458 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Active multiple matrix completion with adaptive confidence sets Locatelli, Andrea Carpentier, Alexandra Valko, Michal Machine Learning 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. |
| title | Active multiple matrix completion with adaptive confidence sets |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2605.02458 |