Pricing with Contextual Elasticity and Heteroscedastic Valuation

Jianyu Xu, Yu-Xiang Wang
Proceedings of the 41st International Conference on Machine Learning, PMLR 235:55286-55304, 2024.

Abstract

We study an online contextual dynamic pricing problem, where customers decide whether to purchase a product based on its features and price. We introduce a novel approach to modeling a customer’s expected demand by incorporating feature-based price elasticity, which can be equivalently represented as a valuation with heteroscedastic noise. To solve the problem, we propose a computationally efficient algorithm called "Pricing with Perturbation (PwP)", which enjoys an $O(\sqrt{dT\log T})$ regret while allowing arbitrary adversarial input context sequences. We also prove a matching lower bound at $\Omega(\sqrt{dT})$ to show the optimality regarding $d$ and $T$ (up to $\log T$ factors). Our results shed light on the relationship between contextual elasticity and heteroscedastic valuation, providing insights for effective and practical pricing strategies.

Cite this Paper

BibTeX
@InProceedings{pmlr-v235-xu24x, title = {Pricing with Contextual Elasticity and Heteroscedastic Valuation}, author = {Xu, Jianyu and Wang, Yu-Xiang}, booktitle = {Proceedings of the 41st International Conference on Machine Learning}, pages = {55286--55304}, year = {2024}, editor = {Salakhutdinov, Ruslan and Kolter, Zico and Heller, Katherine and Weller, Adrian and Oliver, Nuria and Scarlett, Jonathan and Berkenkamp, Felix}, volume = {235}, series = {Proceedings of Machine Learning Research}, month = {21--27 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v235/main/assets/xu24x/xu24x.pdf}, url = {https://proceedings.mlr.press/v235/xu24x.html}, abstract = {We study an online contextual dynamic pricing problem, where customers decide whether to purchase a product based on its features and price. We introduce a novel approach to modeling a customer’s expected demand by incorporating feature-based price elasticity, which can be equivalently represented as a valuation with heteroscedastic noise. To solve the problem, we propose a computationally efficient algorithm called "Pricing with Perturbation (PwP)", which enjoys an $O(\sqrt{dT\log T})$ regret while allowing arbitrary adversarial input context sequences. We also prove a matching lower bound at $\Omega(\sqrt{dT})$ to show the optimality regarding $d$ and $T$ (up to $\log T$ factors). Our results shed light on the relationship between contextual elasticity and heteroscedastic valuation, providing insights for effective and practical pricing strategies.} }
Endnote
%0 Conference Paper %T Pricing with Contextual Elasticity and Heteroscedastic Valuation %A Jianyu Xu %A Yu-Xiang Wang %B Proceedings of the 41st International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2024 %E Ruslan Salakhutdinov %E Zico Kolter %E Katherine Heller %E Adrian Weller %E Nuria Oliver %E Jonathan Scarlett %E Felix Berkenkamp %F pmlr-v235-xu24x %I PMLR %P 55286--55304 %U https://proceedings.mlr.press/v235/xu24x.html %V 235 %X We study an online contextual dynamic pricing problem, where customers decide whether to purchase a product based on its features and price. We introduce a novel approach to modeling a customer’s expected demand by incorporating feature-based price elasticity, which can be equivalently represented as a valuation with heteroscedastic noise. To solve the problem, we propose a computationally efficient algorithm called "Pricing with Perturbation (PwP)", which enjoys an $O(\sqrt{dT\log T})$ regret while allowing arbitrary adversarial input context sequences. We also prove a matching lower bound at $\Omega(\sqrt{dT})$ to show the optimality regarding $d$ and $T$ (up to $\log T$ factors). Our results shed light on the relationship between contextual elasticity and heteroscedastic valuation, providing insights for effective and practical pricing strategies.
APA
Xu, J. & Wang, Y.. (2024). Pricing with Contextual Elasticity and Heteroscedastic Valuation. Proceedings of the 41st International Conference on Machine Learning, in Proceedings of Machine Learning Research 235:55286-55304 Available from https://proceedings.mlr.press/v235/xu24x.html.

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