Thompson Sampling with a Mixture Prior
Joey Hong, Branislav Kveton, Manzil Zaheer, Mohammad Ghavamzadeh, Craig Boutilier
Abstract
We study Thompson sampling (TS) in online decision making, where the uncertain environment is sampled from a mixture distribution. This is relevant in multi-task learning, where a learning agent faces different classes of problems. We incorporate this structure in a natural way by initializing TS with a mixture prior, and call the resulting algorithm MixTS. To analyze MixTS, we develop a novel and general proof technique for analyzing the concentration of mixture distributions. We use it to derive Bayes regret bounds for MixTS in both linear bandits and finite-horizon reinforcement learning (RL). Our regret bounds reflect the structure of the mixture prior, and depend on the number of mixture components and their width. We demonstrate the empirical effectiveness of MixTS in synthetic and real-world experiments.
BibTeX
@InProceedings{pmlr-v151-hong22b,
title = { Thompson Sampling with a Mixture Prior },
author = {Hong, Joey and Kveton, Branislav and Zaheer, Manzil and Ghavamzadeh, Mohammad and Boutilier, Craig},
booktitle = {Proceedings of The 25th International Conference on Artificial Intelligence and Statistics},
pages = {7565--7586},
year = {2022},
editor = {Camps-Valls, Gustau and Ruiz, Francisco J. R. and Valera, Isabel},
volume = {151},
series = {Proceedings of Machine Learning Research},
month = {28--30 Mar},
publisher = {PMLR},
pdf = {https://proceedings.mlr.press/v151/hong22b/hong22b.pdf},
url = {https://proceedings.mlr.press/v151/hong22b.html},
abstract = { We study Thompson sampling (TS) in online decision making, where the uncertain environment is sampled from a mixture distribution. This is relevant in multi-task learning, where a learning agent faces different classes of problems. We incorporate this structure in a natural way by initializing TS with a mixture prior, and call the resulting algorithm MixTS. To analyze MixTS, we develop a novel and general proof technique for analyzing the concentration of mixture distributions. We use it to derive Bayes regret bounds for MixTS in both linear bandits and finite-horizon reinforcement learning (RL). Our regret bounds reflect the structure of the mixture prior, and depend on the number of mixture components and their width. We demonstrate the empirical effectiveness of MixTS in synthetic and real-world experiments. }
}