Semi-Parametric Contextual Pricing Algorithm using Cox Proportional Hazards Model

Young-Geun Choi, Gi-Soo Kim, Yunseo Choi, Wooseong Cho, Myunghee Cho Paik, Min-Hwan Oh
Proceedings of the 40th International Conference on Machine Learning, PMLR 202:5771-5786, 2023.

Abstract

Contextual dynamic pricing is a problem of setting prices based on current contextual information and previous sales history to maximize revenue. A popular approach is to postulate a distribution of customer valuation as a function of contextual information and the baseline valuation. A semi-parametric setting, where the context effect is parametric and the baseline is nonparametric, is of growing interest due to its flexibility. A challenge is that customer valuation is almost never observable in practice and is instead type-I interval censored by the offered price. To address this challenge, we propose a novel semi-parametric contextual pricing algorithm for stochastic contexts, called the epoch-based Cox proportional hazards Contextual Pricing (CoxCP) algorithm. To our best knowledge, our work is the first to employ the Cox model for customer valuation. The CoxCP algorithm has a high-probability regret upper bound of $\tilde{O}( T^{\frac{2}{3}}d )$, where $T$ is the length of horizon and $d$ is the dimension of context. In addition, if the baseline is known, the regret bound can improve to $O( d \log T )$ under certain assumptions. We demonstrate empirically the proposed algorithm performs better than existing semi-parametric contextual pricing algorithms when the model assumptions of all algorithms are correct.

Cite this Paper

BibTeX
@InProceedings{pmlr-v202-choi23c, title = {Semi-Parametric Contextual Pricing Algorithm using {C}ox Proportional Hazards Model}, author = {Choi, Young-Geun and Kim, Gi-Soo and Choi, Yunseo and Cho, Wooseong and Paik, Myunghee Cho and Oh, Min-Hwan}, booktitle = {Proceedings of the 40th International Conference on Machine Learning}, pages = {5771--5786}, year = {2023}, editor = {Krause, Andreas and Brunskill, Emma and Cho, Kyunghyun and Engelhardt, Barbara and Sabato, Sivan and Scarlett, Jonathan}, volume = {202}, series = {Proceedings of Machine Learning Research}, month = {23--29 Jul}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v202/choi23c/choi23c.pdf}, url = {https://proceedings.mlr.press/v202/choi23c.html}, abstract = {Contextual dynamic pricing is a problem of setting prices based on current contextual information and previous sales history to maximize revenue. A popular approach is to postulate a distribution of customer valuation as a function of contextual information and the baseline valuation. A semi-parametric setting, where the context effect is parametric and the baseline is nonparametric, is of growing interest due to its flexibility. A challenge is that customer valuation is almost never observable in practice and is instead type-I interval censored by the offered price. To address this challenge, we propose a novel semi-parametric contextual pricing algorithm for stochastic contexts, called the epoch-based Cox proportional hazards Contextual Pricing (CoxCP) algorithm. To our best knowledge, our work is the first to employ the Cox model for customer valuation. The CoxCP algorithm has a high-probability regret upper bound of $\tilde{O}( T^{\frac{2}{3}}d )$, where $T$ is the length of horizon and $d$ is the dimension of context. In addition, if the baseline is known, the regret bound can improve to $O( d \log T )$ under certain assumptions. We demonstrate empirically the proposed algorithm performs better than existing semi-parametric contextual pricing algorithms when the model assumptions of all algorithms are correct.} }
Endnote
%0 Conference Paper %T Semi-Parametric Contextual Pricing Algorithm using Cox Proportional Hazards Model %A Young-Geun Choi %A Gi-Soo Kim %A Yunseo Choi %A Wooseong Cho %A Myunghee Cho Paik %A Min-Hwan Oh %B Proceedings of the 40th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2023 %E Andreas Krause %E Emma Brunskill %E Kyunghyun Cho %E Barbara Engelhardt %E Sivan Sabato %E Jonathan Scarlett %F pmlr-v202-choi23c %I PMLR %P 5771--5786 %U https://proceedings.mlr.press/v202/choi23c.html %V 202 %X Contextual dynamic pricing is a problem of setting prices based on current contextual information and previous sales history to maximize revenue. A popular approach is to postulate a distribution of customer valuation as a function of contextual information and the baseline valuation. A semi-parametric setting, where the context effect is parametric and the baseline is nonparametric, is of growing interest due to its flexibility. A challenge is that customer valuation is almost never observable in practice and is instead type-I interval censored by the offered price. To address this challenge, we propose a novel semi-parametric contextual pricing algorithm for stochastic contexts, called the epoch-based Cox proportional hazards Contextual Pricing (CoxCP) algorithm. To our best knowledge, our work is the first to employ the Cox model for customer valuation. The CoxCP algorithm has a high-probability regret upper bound of $\tilde{O}( T^{\frac{2}{3}}d )$, where $T$ is the length of horizon and $d$ is the dimension of context. In addition, if the baseline is known, the regret bound can improve to $O( d \log T )$ under certain assumptions. We demonstrate empirically the proposed algorithm performs better than existing semi-parametric contextual pricing algorithms when the model assumptions of all algorithms are correct.
APA
Choi, Y., Kim, G., Choi, Y., Cho, W., Paik, M.C. & Oh, M.. (2023). Semi-Parametric Contextual Pricing Algorithm using Cox Proportional Hazards Model. Proceedings of the 40th International Conference on Machine Learning, in Proceedings of Machine Learning Research 202:5771-5786 Available from https://proceedings.mlr.press/v202/choi23c.html.

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