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Multi-Task Representation Learning for Conservative Linear Bandits

arXiv 2605.12176 ↗First posted 12 May 2026cs.LGcited by 0

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Abstract (arXiv)

This paper presents the Constrained Multi-Task Representation Learning (CMTRL) framework for linear bandits. We consider T linear bandit tasks in a d dimensional space, which share a common low-dimensional representation of dimension r, where r is much smaller than the minimum of d and T. Furthermore, tasks are constrained so that only actions meeting specific safety or performance requirements are allowed, referred to as conservative (safe) bandits. We introduce a novel algorithm, Safe-Alternating projected Gradient Descent and minimization (Safe-AltGDmin), to recover a low-rank feature matrix while satisfying the given constraints. Building on this algorithm, we propose a multi-task representation learning framework for conservative linear bandits and establish theoretical guarantees for its regret and sample complexity bounds. We presented experiments and compared the performance of our algorithm with benchmark algorithms.

Key facts. No citing papers in the map yet (data through 14 Oct 2026). Builds on 41 of its 58 references that are in the map. First posted on arXiv 12 May 2026.

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41 of 58 references.

References · 41

  1. 2021Exploiting Shared Representations for Personalized Federated Learningcited by 541
  2. 2020Few-Shot Learning via Learning the Representation, Provablycited by 214
  3. 2013Bandits with Knapsackscited by 164
  4. 2020Provable Meta-Learning of Linear Representationscited by 161
  5. 2018Nonconvex Optimization Meets Low-Rank Matrix Factorization: An Overviewcited by 160
  6. 2019Batched Multi-armed Bandits Problemcited by 98
  7. 2019Linear Stochastic Bandits Under Safety Constraintscited by 90
  8. 2014Bandits with concave rewards and convex knapsackscited by 83
  9. 2020Sequential Batch Learning in Finite-Action Linear Contextual Banditscited by 63
  10. 2016Conservative Banditscited by 59
  11. 2016Conservative Contextual Linear Banditscited by 57
  12. 2020Impact of Representation Learning in Linear Banditscited by 52
29 more
  1. 2014Resourceful Contextual Banditscited by 45
  2. 2021Near-optimal Representation Learning for Linear Bandits and Linear RLcited by 45
  3. 2022Contextual Bandits with Packing and Covering Constraints: A Modular Lagrangian Approach via Regressioncited by 30
  4. 2015Algorithms with Logarithmic or Sublinear Regret for Constrained Contextual Banditscited by 29
  5. 2021An Efficient Pessimistic-Optimistic Algorithm for Stochastic Linear Bandits with General Constraintscited by 29
  6. 2020Stage-wise Conservative Linear Banditscited by 28
  7. 2019Safe Linear Stochastic Banditscited by 27
  8. 2021Sample Efficient Linear Meta-Learning by Alternating Minimizationcited by 25
  9. 2022On Kernelized Multi-Armed Bandits with Constraintscited by 23
  10. 2022Multi-task Representation Learning with Stochastic Linear Banditscited by 21
  11. 2020Improved Algorithms for Conservative Exploration in Banditscited by 16
  12. 2022Active Learning with Safety Constraintscited by 16
  13. 2016Learning Shared Representations in Multi-task Reinforcement Learningcited by 15
  14. 2020Safe Exploration for Optimizing Contextual Banditscited by 14
  15. 2022Active Multi-Task Representation Learningcited by 14
  16. 2024Offline Multitask Representation Learning for Reinforcement Learningcited by 14
  17. 2021Safe Online Convex Optimization with Unknown Linear Safety Constraintscited by 13
  18. 2022Provable General Function Class Representation Learning in Multitask Bandits and MDPscited by 12
  19. 2024Contextual Bandits with Stage-wise Constraintscited by 12
  20. 2019Thompson Sampling for Contextual Bandit Problems with Auxiliary Safety Constraintscited by 10
  21. 2023Multi-task Representation Learning for Pure Exploration in Linear Banditscited by 6
  22. 2024Fast and Sample Efficient Multi-Task Representation Learning in Stochastic Contextual Banditscited by 6
  23. 2019Phase Transitions in Bandits with Switching Constraintscited by 4
  24. 2022Multi-User Reinforcement Learning with Low Rank Rewardscited by 4
  25. 2024Conservative Contextual Bandits: Beyond Linear Representationscited by 4
  26. 2023Think Before You Duel: Understanding Complexities of Preference Learning under Constrained Resourcescited by 3
  27. 2024Distributed Multi-Task Learning for Stochastic Bandits with Context Distribution and Stage-wise Constraintscited by 2
  28. 2024Noisy Low Rank Column-wise Sensingcited by 2
  29. 2025Beyond Task Diversity: Provable Representation Transfer for Sequential Multi-Task Linear Banditscited by 1

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