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

arXiv: https://arxiv.org/abs/2311.00327 · HTML: https://mlsanity.com/paper/2311.00327/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 35 references that are in the map.
- First posted on arXiv 1 Nov 2023.

## Builds on (most cited first, 17 of 17)

- [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)
- [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)
- [Sub-Gaussian estimators of the mean of a random matrix with heavy-tailed entries](https://mlsanity.com/paper/1605.07129/) (2016)
- [Nearly Optimal Algorithms for Level Set Estimation](https://mlsanity.com/paper/2111.01768/) (2021)
- [Nearly Minimax Algorithms for Linear Bandits with Shared Representation](https://mlsanity.com/paper/2203.15664/) (2022)
- [Chernoff Sampling for Active Testing and Extension to Active Regression](https://mlsanity.com/paper/2012.08073/) (2020)
- [Pure Exploration in Kernel and Neural Bandits](https://mlsanity.com/paper/2106.12034/) (2021)
- [Uncertainty in multitask learning: joint representations for probabilistic MR-only radiotherapy planning](https://mlsanity.com/paper/1806.06595/) (2018)
- [Multi-task Representation Learning for Pure Exploration in Linear Bandits](https://mlsanity.com/paper/2302.04441/) (2023)
- [SPEED: Experimental Design for Policy Evaluation in Linear Heteroscedastic Bandits](https://mlsanity.com/paper/2301.12357/) (2023)

## Built on by (most cited first, 5 of 5)

- [Pretraining Decision Transformers with Reward Prediction for In-Context Multi-task Structured Bandit Learning](https://mlsanity.com/paper/2406.05064/) (2024)
- [Guarantees for Nonlinear Representation Learning: Non-identical Covariates, Dependent Data, Fewer Samples](https://mlsanity.com/paper/2410.11227/) (2024)
- [Efficient Online Lexicographic Generalized Low-Rank Matrix Bandits](https://mlsanity.com/paper/2608.04324/) (2026)
- [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)

## Abstract (arXiv)

We study multi-task representation learning for the problem of pure exploration in bilinear bandits. In bilinear bandits, an action takes the form of a pair of arms from two different entity types and the reward is a bilinear function of the known feature vectors of the arms. In the textitmulti-task bilinear bandit problem, we aim to find optimal actions for multiple tasks that share a common low-dimensional linear representation. The objective is to leverage this characteristic to expedite the process of identifying the best pair of arms for all tasks. We propose the algorithm GOBLIN that uses an experimental design approach to optimize sample allocations for learning the global representation as well as minimize the number of samples needed to identify the optimal pair of arms in individual tasks. To the best of our knowledge, this is the first study to give sample complexity analysis for pure exploration in bilinear bandits with shared representation. Our results demonstrate that by learning the shared representation across tasks, we achieve significantly improved sample complexity compared to the traditional approach of solving tasks independently.