Thompson Sampling for Combinatorial Semi-Bandits

Siwei Wang, Wei Chen
Proceedings of the 35th International Conference on Machine Learning, PMLR 80:5114-5122, 2018.

Abstract

We study the application of the Thompson sampling (TS) methodology to the stochastic combinatorial multi-armed bandit (CMAB) framework. We analyze the standard TS algorithm for the general CMAB, and obtain the first distribution-dependent regret bound of $O(m\log T / \Delta_{\min}) $ for TS under general CMAB, where $m$ is the number of arms, $T$ is the time horizon, and $\Delta_{\min}$ is the minimum gap between the expected reward of the optimal solution and any non-optimal solution. We also show that one cannot use an approximate oracle in TS algorithm for even MAB problems. Then we expand the analysis to matroid bandit, a special case of CMAB and for which we could remove the independence assumption across arms and achieve a better regret bound. Finally, we use some experiments to show the comparison of regrets of CUCB and CTS algorithms.

Cite this Paper

BibTeX
@InProceedings{pmlr-v80-wang18a, title = {Thompson Sampling for Combinatorial Semi-Bandits}, author = {Wang, Siwei and Chen, Wei}, booktitle = {Proceedings of the 35th International Conference on Machine Learning}, pages = {5114--5122}, year = {2018}, editor = {Dy, Jennifer and Krause, Andreas}, volume = {80}, series = {Proceedings of Machine Learning Research}, month = {10--15 Jul}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v80/wang18a/wang18a.pdf}, url = {https://proceedings.mlr.press/v80/wang18a.html}, abstract = {We study the application of the Thompson sampling (TS) methodology to the stochastic combinatorial multi-armed bandit (CMAB) framework. We analyze the standard TS algorithm for the general CMAB, and obtain the first distribution-dependent regret bound of $O(m\log T / \Delta_{\min}) $ for TS under general CMAB, where $m$ is the number of arms, $T$ is the time horizon, and $\Delta_{\min}$ is the minimum gap between the expected reward of the optimal solution and any non-optimal solution. We also show that one cannot use an approximate oracle in TS algorithm for even MAB problems. Then we expand the analysis to matroid bandit, a special case of CMAB and for which we could remove the independence assumption across arms and achieve a better regret bound. Finally, we use some experiments to show the comparison of regrets of CUCB and CTS algorithms.} }
Endnote
%0 Conference Paper %T Thompson Sampling for Combinatorial Semi-Bandits %A Siwei Wang %A Wei Chen %B Proceedings of the 35th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2018 %E Jennifer Dy %E Andreas Krause %F pmlr-v80-wang18a %I PMLR %P 5114--5122 %U https://proceedings.mlr.press/v80/wang18a.html %V 80 %X We study the application of the Thompson sampling (TS) methodology to the stochastic combinatorial multi-armed bandit (CMAB) framework. We analyze the standard TS algorithm for the general CMAB, and obtain the first distribution-dependent regret bound of $O(m\log T / \Delta_{\min}) $ for TS under general CMAB, where $m$ is the number of arms, $T$ is the time horizon, and $\Delta_{\min}$ is the minimum gap between the expected reward of the optimal solution and any non-optimal solution. We also show that one cannot use an approximate oracle in TS algorithm for even MAB problems. Then we expand the analysis to matroid bandit, a special case of CMAB and for which we could remove the independence assumption across arms and achieve a better regret bound. Finally, we use some experiments to show the comparison of regrets of CUCB and CTS algorithms.
APA
Wang, S. & Chen, W.. (2018). Thompson Sampling for Combinatorial Semi-Bandits. Proceedings of the 35th International Conference on Machine Learning, in Proceedings of Machine Learning Research 80:5114-5122 Available from https://proceedings.mlr.press/v80/wang18a.html.

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