Dynamic Planning and Learning under Recovering Rewards

David Simchi-Levi, Zeyu Zheng, Feng Zhu
Proceedings of the 38th International Conference on Machine Learning, PMLR 139:9702-9711, 2021.

Abstract

Motivated by emerging applications such as live-streaming e-commerce, promotions and recommendations, we introduce a general class of multi-armed bandit problems that have the following two features: (i) the decision maker can pull and collect rewards from at most $K$ out of $N$ different arms in each time period; (ii) the expected reward of an arm immediately drops after it is pulled, and then non-parametrically recovers as the idle time increases. With the objective of maximizing expected cumulative rewards over $T$ time periods, we propose, construct and prove performance guarantees for a class of “Purely Periodic Policies”. For the offline problem when all model parameters are known, our proposed policy obtains an approximation ratio that is at the order of $1-\mathcal O(1/\sqrt{K})$, which is asymptotically optimal when $K$ grows to infinity. For the online problem when the model parameters are unknown and need to be learned, we design an Upper Confidence Bound (UCB) based policy that approximately has $\widetilde{\mathcal O}(N\sqrt{T})$ regret against the offline benchmark. Our framework and policy design may have the potential to be adapted into other offline planning and online learning applications with non-stationary and recovering rewards.

Cite this Paper

BibTeX
@InProceedings{pmlr-v139-simchi-levi21a, title = {Dynamic Planning and Learning under Recovering Rewards}, author = {Simchi-Levi, David and Zheng, Zeyu and Zhu, Feng}, booktitle = {Proceedings of the 38th International Conference on Machine Learning}, pages = {9702--9711}, 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/simchi-levi21a/simchi-levi21a.pdf}, url = {https://proceedings.mlr.press/v139/simchi-levi21a.html}, abstract = {Motivated by emerging applications such as live-streaming e-commerce, promotions and recommendations, we introduce a general class of multi-armed bandit problems that have the following two features: (i) the decision maker can pull and collect rewards from at most $K$ out of $N$ different arms in each time period; (ii) the expected reward of an arm immediately drops after it is pulled, and then non-parametrically recovers as the idle time increases. With the objective of maximizing expected cumulative rewards over $T$ time periods, we propose, construct and prove performance guarantees for a class of “Purely Periodic Policies”. For the offline problem when all model parameters are known, our proposed policy obtains an approximation ratio that is at the order of $1-\mathcal O(1/\sqrt{K})$, which is asymptotically optimal when $K$ grows to infinity. For the online problem when the model parameters are unknown and need to be learned, we design an Upper Confidence Bound (UCB) based policy that approximately has $\widetilde{\mathcal O}(N\sqrt{T})$ regret against the offline benchmark. Our framework and policy design may have the potential to be adapted into other offline planning and online learning applications with non-stationary and recovering rewards.} }
Endnote
%0 Conference Paper %T Dynamic Planning and Learning under Recovering Rewards %A David Simchi-Levi %A Zeyu Zheng %A Feng Zhu %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-simchi-levi21a %I PMLR %P 9702--9711 %U https://proceedings.mlr.press/v139/simchi-levi21a.html %V 139 %X Motivated by emerging applications such as live-streaming e-commerce, promotions and recommendations, we introduce a general class of multi-armed bandit problems that have the following two features: (i) the decision maker can pull and collect rewards from at most $K$ out of $N$ different arms in each time period; (ii) the expected reward of an arm immediately drops after it is pulled, and then non-parametrically recovers as the idle time increases. With the objective of maximizing expected cumulative rewards over $T$ time periods, we propose, construct and prove performance guarantees for a class of “Purely Periodic Policies”. For the offline problem when all model parameters are known, our proposed policy obtains an approximation ratio that is at the order of $1-\mathcal O(1/\sqrt{K})$, which is asymptotically optimal when $K$ grows to infinity. For the online problem when the model parameters are unknown and need to be learned, we design an Upper Confidence Bound (UCB) based policy that approximately has $\widetilde{\mathcal O}(N\sqrt{T})$ regret against the offline benchmark. Our framework and policy design may have the potential to be adapted into other offline planning and online learning applications with non-stationary and recovering rewards.
APA
Simchi-Levi, D., Zheng, Z. & Zhu, F.. (2021). Dynamic Planning and Learning under Recovering Rewards. Proceedings of the 38th International Conference on Machine Learning, in Proceedings of Machine Learning Research 139:9702-9711 Available from https://proceedings.mlr.press/v139/simchi-levi21a.html.

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