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Logarithmic Regret in Feature-based Dynamic Pricing

Jianyu Xu, Yu-Xiang Wang

arXiv 20 Feb 2021 · Machine Learning · 1 citations (OpenAlex)

arXiv:2102.10221 · PDF · DOI · OpenAlex · Extracted main text

Abstract

Feature-based dynamic pricing is an increasingly popular model of setting prices for highly differentiated products with applications in digital marketing, online sales, real estate and so on. The problem was formally studied as an online learning problem [Javanmard & Nazerzadeh, 2019] where a seller needs to propose prices on the fly for a sequence of $T$ products based on their features $x$ while having a small regret relative to the best -- "omniscient" -- pricing strategy she could have come up with in hindsight. We revisit this problem and provide two algorithms (EMLP and ONSP) for stochastic and adversarial feature settings, respectively, and prove the optimal $O(d\log{T})$ regret bounds for both. In comparison, the best existing results are $O\left(\min\left{\frac{1}{\lambda_{\min}^2}\log{T}, \sqrt{T}\right}\right)$ and $O(T^{2/3})$ respectively, with $\lambda_{\min}$ being the smallest eigenvalue of $\mathbb{E}[xx^T]$ that could be arbitrarily close to $0$. We also prove an $\Omega(\sqrt{T})$ information-theoretic lower bound for a slightly more general setting, which demonstrates that "knowing-the-demand-curve" leads to an exponential improvement in feature-based dynamic pricing.

Citation extraction

43
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in-text mentions
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appendix boundary found by appendix_command · 45% of the source is main text. Read the extracted text to check this.

Most heavily cited references

The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.

ReferenceIntensityMentionsSectionsMain text
1J. Broder and P. Rusmevichientong (2012) Dynamic pricing under a general parametric choice model1.00053100%
2A. Krishnamurthy, T. Lykouris, C. Podimata, and R. Schapire (2021) Contextual search in the presence of irrational agents0.9507486%
3A. Javanmard and H. Nazerzadeh (2019) Dynamic pricing in high-dimensions0.93717782%
4M. C. Cohen, I. Lobel, and R. Paes Leme (2020) Feature-based dynamic pricing0.92820680%
5R. Kleinberg and T. Leighton (2003) The value of knowing a demand curve: Bounds on regret for online posted-price auctions0.8746467%
6P. Auer, N. Cesa-Bianchi, Y. Freund, and R. E. Schapire (2002) The nonstochastic multiarmed bandit problem0.7374350%
7K. Amin, A. Rostamizadeh, and U. Syed (2014) Repeated contextual auctions with strategic buyers0.73732100%
8A. Liu, R. P. Leme, and J. Schneider (2021) Optimal contextual pricing and extensions0.69351100%
9R. P. Leme and J. Schneider (2018) Contextual search via intrinsic volumes0.58531100%
10A. Agarwal, D. Hsu, S. Kale, J. Langford, L. Li, and R. Schapire (2014) Taming the monster: A fast and simple algorithm for contextual bandits0.5113233%

Showing the top 10 of 43 scored citations.

Cited by, within the corpus

arXiv econ.EM papers that cite this one, ranked by how heavily they lean on it.

Citing paperIntensityMentionsSections
1Pricing with Contextual Elasticity and Heteroscedastic Valuation0.971125
2Towards Agnostic Feature-based Dynamic Pricing: Linear Policies vs Linear Valuation with Unknown Noise0.84333
3Smoothness-Adaptive Dynamic Pricing with Nonparametric Demand Learning0.40511
4Doubly Fair Dynamic Pricing0.00031
5Optimal Contextual Pricing under Agnostic Non-Lipschitz Demand0.00011