# Multi-Task Representation Learning for Conservative Linear Bandits

arXiv: https://arxiv.org/abs/2605.12176 · HTML: https://mlsanity.com/paper/2605.12176/

## 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.

## Builds on (most cited first, 30 of 41)

- [Exploiting Shared Representations for Personalized Federated Learning](https://mlsanity.com/paper/2102.07078/) (2021)
- [Few-Shot Learning via Learning the Representation, Provably](https://mlsanity.com/paper/2002.09434/) (2020)
- [Bandits with Knapsacks](https://mlsanity.com/paper/1305.2545/) (2013)
- [Provable Meta-Learning of Linear Representations](https://mlsanity.com/paper/2002.11684/) (2020)
- [Nonconvex Optimization Meets Low-Rank Matrix Factorization: An Overview](https://mlsanity.com/paper/1809.09573/) (2018)
- [Batched Multi-armed Bandits Problem](https://mlsanity.com/paper/1904.01763/) (2019)
- [Linear Stochastic Bandits Under Safety Constraints](https://mlsanity.com/paper/1908.05814/) (2019)
- [Bandits with concave rewards and convex knapsacks](https://mlsanity.com/paper/1402.5758/) (2014)
- [Sequential Batch Learning in Finite-Action Linear Contextual Bandits](https://mlsanity.com/paper/2004.06321/) (2020)
- [Conservative Bandits](https://mlsanity.com/paper/1602.04282/) (2016)
- [Conservative Contextual Linear Bandits](https://mlsanity.com/paper/1611.06426/) (2016)
- [Impact of Representation Learning in Linear Bandits](https://mlsanity.com/paper/2010.06531/) (2020)
- [Resourceful Contextual Bandits](https://mlsanity.com/paper/1402.6779/) (2014)
- [Near-optimal Representation Learning for Linear Bandits and Linear RL](https://mlsanity.com/paper/2102.04132/) (2021)
- [Contextual Bandits with Packing and Covering Constraints: A Modular Lagrangian Approach via Regression](https://mlsanity.com/paper/2211.07484/) (2022)
- [Algorithms with Logarithmic or Sublinear Regret for Constrained Contextual Bandits](https://mlsanity.com/paper/1504.06937/) (2015)
- [An Efficient Pessimistic-Optimistic Algorithm for Stochastic Linear Bandits with General Constraints](https://mlsanity.com/paper/2102.05295/) (2021)
- [Stage-wise Conservative Linear Bandits](https://mlsanity.com/paper/2010.00081/) (2020)
- [Safe Linear Stochastic Bandits](https://mlsanity.com/paper/1911.09501/) (2019)
- [Sample Efficient Linear Meta-Learning by Alternating Minimization](https://mlsanity.com/paper/2105.08306/) (2021)
- [On Kernelized Multi-Armed Bandits with Constraints](https://mlsanity.com/paper/2203.15589/) (2022)
- [Multi-task Representation Learning with Stochastic Linear Bandits](https://mlsanity.com/paper/2202.10066/) (2022)
- [Improved Algorithms for Conservative Exploration in Bandits](https://mlsanity.com/paper/2002.03221/) (2020)
- [Active Learning with Safety Constraints](https://mlsanity.com/paper/2206.11183/) (2022)
- [Learning Shared Representations in Multi-task Reinforcement Learning](https://mlsanity.com/paper/1603.02041/) (2016)
- [Safe Exploration for Optimizing Contextual Bandits](https://mlsanity.com/paper/2002.00467/) (2020)
- [Active Multi-Task Representation Learning](https://mlsanity.com/paper/2202.00911/) (2022)
- [Offline Multitask Representation Learning for Reinforcement Learning](https://mlsanity.com/paper/2403.11574/) (2024)
- [Safe Online Convex Optimization with Unknown Linear Safety Constraints](https://mlsanity.com/paper/2111.07430/) (2021)
- [Provable General Function Class Representation Learning in Multitask Bandits and MDPs](https://mlsanity.com/paper/2205.15701/) (2022)

## 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.