# Beyond Task Diversity: Provable Representation Transfer for Sequential Multi-Task Linear Bandits

arXiv: https://arxiv.org/abs/2501.13390 · HTML: https://mlsanity.com/paper/2501.13390/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 21 references that are in the map.
- First posted on arXiv 23 Jan 2025.

## Builds on (most cited first, 9 of 9)

- [Provable Meta-Learning of Linear Representations](https://mlsanity.com/paper/2002.11684/) (2020)
- [Impact of Representation Learning in Linear Bandits](https://mlsanity.com/paper/2010.06531/) (2020)
- [Near-optimal Representation Learning for Linear Bandits and Linear RL](https://mlsanity.com/paper/2102.04132/) (2021)
- [Multi-task Representation Learning with Stochastic Linear Bandits](https://mlsanity.com/paper/2202.10066/) (2022)
- [Nearly Minimax Algorithms for Linear Bandits with Shared Representation](https://mlsanity.com/paper/2203.15664/) (2022)
- [Non-Stationary Representation Learning in Sequential Linear Bandits](https://mlsanity.com/paper/2201.04805/) (2022)
- [Non-stationary Bandits and Meta-Learning with a Small Set of Optimal Arms](https://mlsanity.com/paper/2202.13001/) (2022)
- [Meta-Learning Adversarial Bandits](https://mlsanity.com/paper/2205.14128/) (2022)
- [Meta Learning in Bandits within Shared Affine Subspaces](https://mlsanity.com/paper/2404.00688/) (2024)

## Built on by (most cited first, 1 of 1)

- [Multi-Task Representation Learning for Conservative Linear Bandits](https://mlsanity.com/paper/2605.12176/) (2026)

## Abstract (arXiv)

We study lifelong learning in linear bandits, where a learner interacts with a sequence of linear bandit tasks whose parameters lie in an m-dimensional subspace of ℝd, thereby sharing a low-rank representation. Current literature typically assumes that the tasks are diverse, i.e., their parameters uniformly span the m-dimensional subspace. This assumption allows the low-rank representation to be learned before all tasks are revealed, which can be unrealistic in real-world applications. In this work, we present the first nontrivial result for sequential multi-task linear bandits without the task diversity assumption. We develop an algorithm that efficiently learns and transfers low-rank representations. When facing N tasks, each played over τ rounds, our algorithm achieves a regret guarantee of tildeObig (Nm √τ + N^frac23 τ^frac23 d mfrac13 + Nd2 + τ m d big) under the ellipsoid action set assumption. This result can significantly improve upon the baseline of tildeO left (Nd √τright) that does not leverage the low-rank structure when the number of tasks N is sufficiently large and m ll d. We also demonstrate empirically on synthetic data that our algorithm outperforms baseline algorithms, which rely on the task diversity assumption.