# Multi-task Representation Learning with Stochastic Linear Bandits

arXiv: https://arxiv.org/abs/2202.10066 · HTML: https://mlsanity.com/paper/2202.10066/

## Key facts

- Cited by 21 papers in the map (data through 14 Oct 2026).
- Builds on 18 of its 53 references that are in the map.
- First posted on arXiv 21 Feb 2022.

## Builds on (most cited first, 18 of 18)

- [Beyond UCB: Optimal and Efficient Contextual Bandits with Regression Oracles](https://mlsanity.com/paper/2002.04926/) (2020)
- [The Benefit of Multitask Representation Learning](https://mlsanity.com/paper/1505.06279/) (2015)
- [Provable Meta-Learning of Linear Representations](https://mlsanity.com/paper/2002.11684/) (2020)
- [Mostly Exploration-Free Algorithms for Contextual Bandits](https://mlsanity.com/paper/1704.09011/) (2017)
- [Meta-Thompson Sampling](https://mlsanity.com/paper/2102.06129/) (2021)
- [High-Dimensional Sparse Linear Bandits](https://mlsanity.com/paper/2011.04020/) (2020)
- [Impact of Representation Learning in Linear Bandits](https://mlsanity.com/paper/2010.06531/) (2020)
- [Doubly-Robust Lasso Bandit](https://mlsanity.com/paper/1907.11362/) (2019)
- [Low-Rank Generalized Linear Bandit Problems](https://mlsanity.com/paper/2006.02948/) (2020)
- [Meta-learning with Stochastic Linear Bandits](https://mlsanity.com/paper/2005.08531/) (2020)
- [Near-optimal Representation Learning for Linear Bandits and Linear RL](https://mlsanity.com/paper/2102.04132/) (2021)
- [Sparsity-Agnostic Lasso Bandit](https://mlsanity.com/paper/2007.08477/) (2020)
- [Bayesian decision-making under misspecified priors with applications to meta-learning](https://mlsanity.com/paper/2107.01509/) (2021)
- [No Regrets for Learning the Prior in Bandits](https://mlsanity.com/paper/2107.06196/) (2021)
- [Stochastic Low-Rank Bandits](https://mlsanity.com/paper/1712.04644/) (2017)
- [Incremental Learning-to-Learn with Statistical Guarantees](https://mlsanity.com/paper/1803.08089/) (2018)
- [Thresholded Lasso Bandit](https://mlsanity.com/paper/2010.11994/) (2020)
- [Efficient Linear Bandits through Matrix Sketching](https://mlsanity.com/paper/1809.11033/) (2018)

## Built on by (most cited first, 21 of 21)

- [Provable Benefit of Multitask Representation Learning in Reinforcement Learning](https://mlsanity.com/paper/2206.05900/) (2022)
- [Mixed-Effect Thompson Sampling](https://mlsanity.com/paper/2205.15124/) (2022)
- [Online Clustering of Bandits with Misspecified User Models](https://mlsanity.com/paper/2310.02717/) (2023)
- [Optimal Multitask Linear Regression and Contextual Bandits under Sparse Heterogeneity](https://mlsanity.com/paper/2306.06291/) (2023)
- [Meta Representation Learning with Contextual Linear Bandits](https://mlsanity.com/paper/2205.15100/) (2022)
- [Multi-task Representation Learning for Pure Exploration in Linear Bandits](https://mlsanity.com/paper/2302.04441/) (2023)
- [Fast and Sample Efficient Multi-Task Representation Learning in Stochastic Contextual Bandits](https://mlsanity.com/paper/2410.02068/) (2024)
- [Diffusion Models Meet Contextual Bandits](https://mlsanity.com/paper/2402.10028/) (2024)
- [A randomized algorithm to solve reduced rank operator regression](https://mlsanity.com/paper/2312.17348/) (2023)
- [Meta Learning in Bandits within Shared Affine Subspaces](https://mlsanity.com/paper/2404.00688/) (2024)
- [Distributed Multi-Task Learning for Stochastic Bandits with Context Distribution and Stage-wise Constraints](https://mlsanity.com/paper/2401.11563/) (2024)
- [New Classes of the Greedy-Applicable Arm Feature Distributions in the Sparse Linear Bandit Problem](https://mlsanity.com/paper/2312.12400/) (2023)
- [Open Problem: Active Representation Learning](https://mlsanity.com/paper/2406.03845/) (2024)
- [Exploiting Adjacent Similarity in Multi-Armed Bandit Tasks via Transfer of Reward Samples](https://mlsanity.com/paper/2409.19975/) (2024)
- [Beyond Task Diversity: Provable Representation Transfer for Sequential Multi-Task Linear Bandits](https://mlsanity.com/paper/2501.13390/) (2025)
- [Towards Understanding the Benefit of Multitask Representation Learning in Decision Process](https://mlsanity.com/paper/2503.00345/) (2025)
- [A conversion theorem and minimax optimality for continuum contextual bandits](https://mlsanity.com/paper/2406.05714/) (2024)
- [Anomaly Detection in Networked Bandits](https://mlsanity.com/paper/2508.20076/) (2025)
- [RepUCB: Representation Learning-Based UCB for Heterogeneous Multi-Task Linear Bandits](https://mlsanity.com/paper/2604.00531/) (2026)
- [Multi-Task Representation Learning for Conservative Linear Bandits](https://mlsanity.com/paper/2605.12176/) (2026)
- [On-Policy and Off-Policy Learning for Large Action Spaces](https://mlsanity.com/paper/2607.28408/) (2026)

## Abstract (arXiv)

We study the problem of transfer-learning in the setting of stochastic linear bandit tasks. We consider that a low dimensional linear representation is shared across the tasks, and study the benefit of learning this representation in the multi-task learning setting. Following recent results to design 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. We derive an upper bound on the multi-task regret of our policy, which is, up to logarithmic factors, of order √NdT(T+d)r, 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 compared to the baseline Td√N obtained by solving each task independently. We also provide a lower bound to the multi-task regret. Finally, we corroborate our theoretical findings with preliminary experiments on synthetic data.