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Multi-task Representation Learning with Stochastic Linear Bandits

Cella, L; Lounici, K; Pacreau, G; Pontil, M; (2023) Multi-task Representation Learning with Stochastic Linear Bandits. In: Proceedings of Machine Learning Research (PMLR). (pp. pp. 4822-4847). MLResearchPress Green open access

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Abstract

We study the problem of transfer-learning in the setting of stochastic linear contextual bandit tasks. We consider that a low dimensional linear representation is shared across the tasks, and study the benefit of learning the tasks jointly. Following recent results to design Lasso stochastic bandit policies, we propose an efficient greedy policy based on trace norm regularization. It implicitly learns a low dimensional representation by encouraging the matrix formed by the task regression vectors to be of low rank. Unlike previous work in the literature, our policy does not need to know the rank of the underlying matrix, nor does it requires the covariance of the arms distribution to be invertible. We derive an upper bound on the multi-task regret of our policy, which is, up to logarithmic factors, of order T √rN + √rNTd, where T is the number of tasks, r the rank, d the number of variables and N the number of rounds per task. We show the benefit of our strategy over an independent task learning baseline, which has a worse regret of order T √dN. We also argue that our policy is minimax optimal and, when T ≥ d, has a multi-task regret which is comparable to the regret of an oracle policy which knows the true underlying representation.

Type: Proceedings paper
Title: Multi-task Representation Learning with Stochastic Linear Bandits
Event: The 26th International Conference on Artificial Intelligence and Statistics
Open access status: An open access version is available from UCL Discovery
Publisher version: https://proceedings.mlr.press/v206/cella23a.html
Language: English
Additional information: This work is licensed under a Creative Commons Attribution 4.0 International License. The images or other third-party material in this article are included in the Creative Commons license, unless indicated otherwise in the credit line; if the material is not included under the Creative Commons license, users will need to obtain permission from the license holder to reproduce the material. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/
UCL classification: UCL
UCL > Provost and Vice Provost Offices > UCL BEAMS
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science > Dept of Computer Science
URI: https://discovery-pp.ucl.ac.uk/id/eprint/10174540
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