Stochastic Multi-Armed Bandits with Unrestricted Delay Distributions

Tal Lancewicki, Shahar Segal, Tomer Koren, Yishay Mansour
Proceedings of the 38th International Conference on Machine Learning, PMLR 139:5969-5978, 2021.

Abstract

We study the stochastic Multi-Armed Bandit (MAB) problem with random delays in the feedback received by the algorithm. We consider two settings: the {\it reward dependent} delay setting, where realized delays may depend on the stochastic rewards, and the {\it reward-independent} delay setting. Our main contribution is algorithms that achieve near-optimal regret in each of the settings, with an additional additive dependence on the quantiles of the delay distribution. Our results do not make any assumptions on the delay distributions: in particular, we do not assume they come from any parametric family of distributions and allow for unbounded support and expectation; we further allow for the case of infinite delays where the algorithm might occasionally not observe any feedback.

Cite this Paper

BibTeX
@InProceedings{pmlr-v139-lancewicki21a, title = {Stochastic Multi-Armed Bandits with Unrestricted Delay Distributions}, author = {Lancewicki, Tal and Segal, Shahar and Koren, Tomer and Mansour, Yishay}, booktitle = {Proceedings of the 38th International Conference on Machine Learning}, pages = {5969--5978}, year = {2021}, editor = {Meila, Marina and Zhang, Tong}, volume = {139}, series = {Proceedings of Machine Learning Research}, month = {18--24 Jul}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v139/lancewicki21a/lancewicki21a.pdf}, url = {https://proceedings.mlr.press/v139/lancewicki21a.html}, abstract = {We study the stochastic Multi-Armed Bandit (MAB) problem with random delays in the feedback received by the algorithm. We consider two settings: the {\it reward dependent} delay setting, where realized delays may depend on the stochastic rewards, and the {\it reward-independent} delay setting. Our main contribution is algorithms that achieve near-optimal regret in each of the settings, with an additional additive dependence on the quantiles of the delay distribution. Our results do not make any assumptions on the delay distributions: in particular, we do not assume they come from any parametric family of distributions and allow for unbounded support and expectation; we further allow for the case of infinite delays where the algorithm might occasionally not observe any feedback.} }
Endnote
%0 Conference Paper %T Stochastic Multi-Armed Bandits with Unrestricted Delay Distributions %A Tal Lancewicki %A Shahar Segal %A Tomer Koren %A Yishay Mansour %B Proceedings of the 38th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2021 %E Marina Meila %E Tong Zhang %F pmlr-v139-lancewicki21a %I PMLR %P 5969--5978 %U https://proceedings.mlr.press/v139/lancewicki21a.html %V 139 %X We study the stochastic Multi-Armed Bandit (MAB) problem with random delays in the feedback received by the algorithm. We consider two settings: the {\it reward dependent} delay setting, where realized delays may depend on the stochastic rewards, and the {\it reward-independent} delay setting. Our main contribution is algorithms that achieve near-optimal regret in each of the settings, with an additional additive dependence on the quantiles of the delay distribution. Our results do not make any assumptions on the delay distributions: in particular, we do not assume they come from any parametric family of distributions and allow for unbounded support and expectation; we further allow for the case of infinite delays where the algorithm might occasionally not observe any feedback.
APA
Lancewicki, T., Segal, S., Koren, T. & Mansour, Y.. (2021). Stochastic Multi-Armed Bandits with Unrestricted Delay Distributions. Proceedings of the 38th International Conference on Machine Learning, in Proceedings of Machine Learning Research 139:5969-5978 Available from https://proceedings.mlr.press/v139/lancewicki21a.html.

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