Information Directed Sampling for Sparse Linear Bandits
Botao Hao, Tor Lattimore, Wei Deng
Abstract
Stochastic sparse linear bandits offer a practical model for high-dimensional online decision-making problems and have a rich information-regret structure. In this work we explore the use of information-directed sampling (IDS), which naturally balances the information-regret trade-off. We develop a class of information-theoretic Bayesian regret bounds that nearly match existing lower bounds on a variety of problem instances, demonstrating the adaptivity of IDS. To efficiently implement sparse IDS, we propose an empirical Bayesian approach for sparse posterior sampling using a spike-and-slab Gaussian-Laplace prior. Numerical results demonstrate significant regret reductions by sparse IDS relative to several baselines.
BibTeX
@inproceedings{
hao2021information,
title={Information Directed Sampling for Sparse Linear Bandits},
author={Botao Hao and Tor Lattimore and Wei Deng},
booktitle={Advances in Neural Information Processing Systems},
editor={A. Beygelzimer and Y. Dauphin and P. Liang and J. Wortman Vaughan},
year={2021},
url={https://openreview.net/forum?id=syIj5ggwCYJ}
}