Online Learning and Pricing with Reusable Resources: Linear Bandits with Sub-Exponential Rewards

Huiwen Jia, Cong Shi, Siqian Shen
Proceedings of the 39th International Conference on Machine Learning, PMLR 162:10135-10160, 2022.

Abstract

We consider a price-based revenue management problem with reusable resources over a finite time horizon $T$. The problem finds important applications in car/bicycle rental, ridesharing, cloud computing, and hospitality management. Customers arrive following a price-dependent Poisson process and each customer requests one unit of $c$ homogeneous reusable resources. If there is an available unit, the customer gets served within a price-dependent exponentially distributed service time; otherwise, she waits in a queue until the next available unit. The decision maker assumes that the inter-arrival and service intervals have an unknown linear dependence on a $d_f$-dimensional feature vector associated with the posted price. We propose a rate-optimal online learning and pricing algorithm, termed Batch Linear Confidence Bound (BLinUCB), and prove that the cumulative regret is $\tilde{O}( d_f \sqrt{T } )$. In establishing the regret, we bound the transient system performance upon price changes via a coupling argument, and also generalize linear bandits to accommodate sub-exponential rewards.

Cite this Paper

BibTeX
@InProceedings{pmlr-v162-jia22c, title = {Online Learning and Pricing with Reusable Resources: Linear Bandits with Sub-Exponential Rewards}, author = {Jia, Huiwen and Shi, Cong and Shen, Siqian}, booktitle = {Proceedings of the 39th International Conference on Machine Learning}, pages = {10135--10160}, year = {2022}, editor = {Chaudhuri, Kamalika and Jegelka, Stefanie and Song, Le and Szepesvari, Csaba and Niu, Gang and Sabato, Sivan}, volume = {162}, series = {Proceedings of Machine Learning Research}, month = {17--23 Jul}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v162/jia22c/jia22c.pdf}, url = {https://proceedings.mlr.press/v162/jia22c.html}, abstract = {We consider a price-based revenue management problem with reusable resources over a finite time horizon $T$. The problem finds important applications in car/bicycle rental, ridesharing, cloud computing, and hospitality management. Customers arrive following a price-dependent Poisson process and each customer requests one unit of $c$ homogeneous reusable resources. If there is an available unit, the customer gets served within a price-dependent exponentially distributed service time; otherwise, she waits in a queue until the next available unit. The decision maker assumes that the inter-arrival and service intervals have an unknown linear dependence on a $d_f$-dimensional feature vector associated with the posted price. We propose a rate-optimal online learning and pricing algorithm, termed Batch Linear Confidence Bound (BLinUCB), and prove that the cumulative regret is $\tilde{O}( d_f \sqrt{T } )$. In establishing the regret, we bound the transient system performance upon price changes via a coupling argument, and also generalize linear bandits to accommodate sub-exponential rewards.} }
Endnote
%0 Conference Paper %T Online Learning and Pricing with Reusable Resources: Linear Bandits with Sub-Exponential Rewards %A Huiwen Jia %A Cong Shi %A Siqian Shen %B Proceedings of the 39th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2022 %E Kamalika Chaudhuri %E Stefanie Jegelka %E Le Song %E Csaba Szepesvari %E Gang Niu %E Sivan Sabato %F pmlr-v162-jia22c %I PMLR %P 10135--10160 %U https://proceedings.mlr.press/v162/jia22c.html %V 162 %X We consider a price-based revenue management problem with reusable resources over a finite time horizon $T$. The problem finds important applications in car/bicycle rental, ridesharing, cloud computing, and hospitality management. Customers arrive following a price-dependent Poisson process and each customer requests one unit of $c$ homogeneous reusable resources. If there is an available unit, the customer gets served within a price-dependent exponentially distributed service time; otherwise, she waits in a queue until the next available unit. The decision maker assumes that the inter-arrival and service intervals have an unknown linear dependence on a $d_f$-dimensional feature vector associated with the posted price. We propose a rate-optimal online learning and pricing algorithm, termed Batch Linear Confidence Bound (BLinUCB), and prove that the cumulative regret is $\tilde{O}( d_f \sqrt{T } )$. In establishing the regret, we bound the transient system performance upon price changes via a coupling argument, and also generalize linear bandits to accommodate sub-exponential rewards.
APA
Jia, H., Shi, C. & Shen, S.. (2022). Online Learning and Pricing with Reusable Resources: Linear Bandits with Sub-Exponential Rewards. Proceedings of the 39th International Conference on Machine Learning, in Proceedings of Machine Learning Research 162:10135-10160 Available from https://proceedings.mlr.press/v162/jia22c.html.

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