# Multi-task Representation Learning for Pure Exploration in Linear Bandits

arXiv: https://arxiv.org/abs/2302.04441 · HTML: https://mlsanity.com/paper/2302.04441/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 31 of its 60 references that are in the map.
- First posted on arXiv 9 Feb 2023.

## Builds on (most cited first, 30 of 31)

- [An Introduction to Matrix Concentration Inequalities](https://mlsanity.com/paper/1501.01571/) (2015)
- [Few-Shot Learning via Learning the Representation, Provably](https://mlsanity.com/paper/2002.09434/) (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)
- [Best-Arm Identification in Linear Bandits](https://mlsanity.com/paper/1409.6110/) (2014)
- [Sequential Experimental Design for Transductive Linear Bandits](https://mlsanity.com/paper/1906.08399/) (2019)
- [Optimal Best-arm Identification in Linear Bandits](https://mlsanity.com/paper/2006.16073/) (2020)
- [Gamification of Pure Exploration for Linear Bandits](https://mlsanity.com/paper/2007.00953/) (2020)
- [Bilinear Bandits with Low-rank Structure](https://mlsanity.com/paper/1901.02470/) (2019)
- [Impact of Representation Learning in Linear Bandits](https://mlsanity.com/paper/2010.06531/) (2020)
- [Low-Rank Generalized Linear Bandit Problems](https://mlsanity.com/paper/2006.02948/) (2020)
- [An Empirical Process Approach to the Union Bound: Practical Algorithms for Combinatorial and Linear Bandits](https://mlsanity.com/paper/2006.11685/) (2020)
- [Near-optimal Representation Learning for Linear Bandits and Linear RL](https://mlsanity.com/paper/2102.04132/) (2021)
- [Fully adaptive algorithm for pure exploration in linear bandits](https://mlsanity.com/paper/1710.05552/) (2017)
- [Provable Benefits of Representational Transfer in Reinforcement Learning](https://mlsanity.com/paper/2205.14571/) (2022)
- [On the Power of Multitask Representation Learning in Linear MDP](https://mlsanity.com/paper/2106.08053/) (2021)
- [Provable Benefit of Multitask Representation Learning in Reinforcement Learning](https://mlsanity.com/paper/2206.05900/) (2022)
- [Multi-task Representation Learning with Stochastic Linear Bandits](https://mlsanity.com/paper/2202.10066/) (2022)
- [Design of Experiments for Stochastic Contextual Linear Bandits](https://mlsanity.com/paper/2107.09912/) (2021)
- [Efficient and Parsimonious Agnostic Active Learning](https://mlsanity.com/paper/1506.08669/) (2015)
- [Provably Efficient Multi-Task Reinforcement Learning with Model Transfer](https://mlsanity.com/paper/2107.08622/) (2021)
- [Nearly Minimax Algorithms for Linear Bandits with Shared Representation](https://mlsanity.com/paper/2203.15664/) (2022)
- [Instance-optimal PAC Algorithms for Contextual Bandits](https://mlsanity.com/paper/2207.02357/) (2022)
- [Stochastic Linear Bandits with Hidden Low Rank Structure](https://mlsanity.com/paper/1901.09490/) (2019)
- [Optimal Gradient-based Algorithms for Non-concave Bandit Optimization](https://mlsanity.com/paper/2107.04518/) (2021)
- [Non-Stationary Representation Learning in Sequential Linear Bandits](https://mlsanity.com/paper/2201.04805/) (2022)
- [Bandit Phase Retrieval](https://mlsanity.com/paper/2106.01660/) (2021)
- [Provable General Function Class Representation Learning in Multitask Bandits and MDPs](https://mlsanity.com/paper/2205.15701/) (2022)
- [Uncertainty in multitask learning: joint representations for probabilistic MR-only radiotherapy planning](https://mlsanity.com/paper/1806.06595/) (2018)
- [Meta Representation Learning with Contextual Linear Bandits](https://mlsanity.com/paper/2205.15100/) (2022)

## Built on by (most cited first, 6 of 6)

- [Pretraining Decision Transformers with Reward Prediction for In-Context Multi-task Structured Bandit Learning](https://mlsanity.com/paper/2406.05064/) (2024)
- [Multi-task Representation Learning for Pure Exploration in Bilinear Bandits](https://mlsanity.com/paper/2311.00327/) (2023)
- [Guarantees for Nonlinear Representation Learning: Non-identical Covariates, Dependent Data, Fewer Samples](https://mlsanity.com/paper/2410.11227/) (2024)
- [BandiK: Efficient Multi-Task Decomposition Using a Multi-Bandit Framework](https://mlsanity.com/paper/2512.24708/) (2025)
- [Semi-overlapping Multi-bandit Best Arm Identification for Sequential Support Network Learning](https://mlsanity.com/paper/2512.24959/) (2025)
- [Multi-Task Representation Learning for Conservative Linear Bandits](https://mlsanity.com/paper/2605.12176/) (2026)

## Abstract (arXiv)

Despite the recent success of representation learning in sequential decision making, the study of the pure exploration scenario (i.e., identify the best option and minimize the sample complexity) is still limited. In this paper, we study multi-task representation learning for best arm identification in linear bandits (RepBAI-LB) and best policy identification in contextual linear bandits (RepBPI-CLB), two popular pure exploration settings with wide applications, e.g., clinical trials and web content optimization. In these two problems, all tasks share a common low-dimensional linear representation, and our goal is to leverage this feature to accelerate the best arm (policy) identification process for all tasks. For these problems, we design computationally and sample efficient algorithms DouExpDes and C-DouExpDes, which perform double experimental designs to plan optimal sample allocations for learning the global representation. We show that by learning the common representation among tasks, our sample complexity is significantly better than that of the native approach which solves tasks independently. To the best of our knowledge, this is the first work to demonstrate the benefits of representation learning for multi-task pure exploration.