@inproceedings{
duong2024beyond,
title={Beyond task diversity: provable representation transfer for sequential multitask linear bandits},
author={Thang Duong and Zhi Wang and Chicheng Zhang},
booktitle={The Thirty-eighth Annual Conference on Neural Information Processing Systems},
year={2024},
url={https://openreview.net/forum?id=2kZMtdjzSV}
}
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 $\mathbb{R}^d$, 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 $\tau$ rounds, our algorithm achieves a regret guarantee of $\tilde{O}\big (Nm \sqrt{\tau} + N^{\frac{2}{3}} \tau^{\frac{2}{3}} d m^{\frac13} + Nd^2 + \tau m d \big)$ under the ellipsoid action set assumption.
Beyond task diversity: provable representation transfer for sequential multitask linear bandits
Thang Duong Zhi Wang Chicheng Zhang