Towards Agnostic Feature-based Dynamic Pricing: Linear Policies vs Linear Valuation with Unknown Noise

Jianyu Xu, Yu-Xiang Wang
Proceedings of The 25th International Conference on Artificial Intelligence and Statistics, PMLR 151:9643-9662, 2022.

Abstract

In feature-based dynamic pricing, a seller sets appropriate prices for a sequence of products (described by feature vectors) on the fly by learning from the binary outcomes of previous sales sessions ("Sold" if valuation $\geq$ price, and "Not Sold" otherwise). Existing works either assume noiseless linear valuation or precisely-known noise distribution, which limits the applicability of those algorithms in practice when these assumptions are hard to verify. In this work, we study two more agnostic models: (a) a "linear policy" problem where we aim at competing with the best linear pricing policy while making no assumptions on the data, and (b) a "linear noisy valuation" problem where the random valuation is linear plus an unknown and assumption-free noise. For the former model, we show a $\Theta(d^{1/3}T^{2/3})$ minimax regret up to logarithmic factors. For the latter model, we present an algorithm that achieves an $O(T^{3/4})$ regret and improve the best-known lower bound from $Omega(T^{3/5})$ to $\Omega(T^{2/3})$. These results demonstrate that no-regret learning is possible for feature-based dynamic pricing under weak assumptions, but also reveal a disappointing fact that the seemingly richer pricing feedback is not significantly more useful than the bandit-feedback in regret reduction.

Cite this Paper

BibTeX
@InProceedings{pmlr-v151-xu22d, title = { Towards Agnostic Feature-based Dynamic Pricing: Linear Policies vs Linear Valuation with Unknown Noise }, author = {Xu, Jianyu and Wang, Yu-Xiang}, booktitle = {Proceedings of The 25th International Conference on Artificial Intelligence and Statistics}, pages = {9643--9662}, year = {2022}, editor = {Camps-Valls, Gustau and Ruiz, Francisco J. R. and Valera, Isabel}, volume = {151}, series = {Proceedings of Machine Learning Research}, month = {28--30 Mar}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v151/xu22d/xu22d.pdf}, url = {https://proceedings.mlr.press/v151/xu22d.html}, abstract = { In feature-based dynamic pricing, a seller sets appropriate prices for a sequence of products (described by feature vectors) on the fly by learning from the binary outcomes of previous sales sessions ("Sold" if valuation $\geq$ price, and "Not Sold" otherwise). Existing works either assume noiseless linear valuation or precisely-known noise distribution, which limits the applicability of those algorithms in practice when these assumptions are hard to verify. In this work, we study two more agnostic models: (a) a "linear policy" problem where we aim at competing with the best linear pricing policy while making no assumptions on the data, and (b) a "linear noisy valuation" problem where the random valuation is linear plus an unknown and assumption-free noise. For the former model, we show a $\Theta(d^{1/3}T^{2/3})$ minimax regret up to logarithmic factors. For the latter model, we present an algorithm that achieves an $O(T^{3/4})$ regret and improve the best-known lower bound from $Omega(T^{3/5})$ to $\Omega(T^{2/3})$. These results demonstrate that no-regret learning is possible for feature-based dynamic pricing under weak assumptions, but also reveal a disappointing fact that the seemingly richer pricing feedback is not significantly more useful than the bandit-feedback in regret reduction. } }
Endnote
%0 Conference Paper %T Towards Agnostic Feature-based Dynamic Pricing: Linear Policies vs Linear Valuation with Unknown Noise %A Jianyu Xu %A Yu-Xiang Wang %B Proceedings of The 25th International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2022 %E Gustau Camps-Valls %E Francisco J. R. Ruiz %E Isabel Valera %F pmlr-v151-xu22d %I PMLR %P 9643--9662 %U https://proceedings.mlr.press/v151/xu22d.html %V 151 %X In feature-based dynamic pricing, a seller sets appropriate prices for a sequence of products (described by feature vectors) on the fly by learning from the binary outcomes of previous sales sessions ("Sold" if valuation $\geq$ price, and "Not Sold" otherwise). Existing works either assume noiseless linear valuation or precisely-known noise distribution, which limits the applicability of those algorithms in practice when these assumptions are hard to verify. In this work, we study two more agnostic models: (a) a "linear policy" problem where we aim at competing with the best linear pricing policy while making no assumptions on the data, and (b) a "linear noisy valuation" problem where the random valuation is linear plus an unknown and assumption-free noise. For the former model, we show a $\Theta(d^{1/3}T^{2/3})$ minimax regret up to logarithmic factors. For the latter model, we present an algorithm that achieves an $O(T^{3/4})$ regret and improve the best-known lower bound from $Omega(T^{3/5})$ to $\Omega(T^{2/3})$. These results demonstrate that no-regret learning is possible for feature-based dynamic pricing under weak assumptions, but also reveal a disappointing fact that the seemingly richer pricing feedback is not significantly more useful than the bandit-feedback in regret reduction.
APA
Xu, J. & Wang, Y.. (2022). Towards Agnostic Feature-based Dynamic Pricing: Linear Policies vs Linear Valuation with Unknown Noise . Proceedings of The 25th International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 151:9643-9662 Available from https://proceedings.mlr.press/v151/xu22d.html.

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