Optimal Nonparametric Dynamic Pricing with Censored Demand and Adversarial Inventory

Mengxiao Zhang; Yingfei Wang; Haipeng Luo

doi:10.48550/arxiv.2609.32949

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Optimal Nonparametric Dynamic Pricing with Censored Demand and Adversarial Inventory

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Optimal Nonparametric Dynamic Pricing with Censored Demand and Adversarial Inventory

Mengxiao Zhang, Yingfei Wang and Haipeng Luo

arXiv

09/26/2026

DOI: 10.48550/arxiv.2609.32949

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Preprint (Author's original) This preprint has not been evaluated by subject experts through peer review. Preprints may undergo extensive changes and/or become peer-reviewed journal articles. Open Access

Abstract

We study online dynamic pricing with censored demand, where an arbitrary inventory level is revealed before pricing and may adapt to past observations, while demand follows an unknown, price-dependent distribution that is stationary over time. For a horizon ofTrounds, Xu et al. [2026] achieved\widetilde{𝓞}{(}{√T̅})regret under restrictive structural assumptions including linear demand, price-independent additive noise, and conditions relating inventory levels to the noise support. Our first contribution is to extend this framework to a substantially more general and statistically harder nonparametric setting, requiring only the natural assumption that expected sales are nonincreasing in price and allowing nonlinear demand curves and price-dependent noise. For this model, we first propose a simple baseline, Double-Grid-UCB, which discretizes both price and inventory and achieves\widetilde{𝓞}{(}{T}^(3/4))expected regret using separate revenue estimates for each price-inventory grid pair. Then, we develop Threshold-UCB, which improves the expected regret to\widetilde{𝓞}{(}{T}^(2/3)) . Unlike Double-Grid-UCB, Threshold-UCB reuses sales observations across inventory levels through shared estimates of demand-tail probabilities, allowing the same data to support revenue upper bounds for multiple inventories rather than a single inventory bin. We also complement this upper bound with anΩ(T^(2/3))lower bound via a reduction from stochastic posted pricing, establishing its minimax optimality. Finally, extensive experiments across inventory processes, demand functions, and noise models demonstrate consistently superior performance of Threshold-UCB over benchmark algorithms.

Computer Science - Learning

Details

Title: Subtitle: Optimal Nonparametric Dynamic Pricing with Censored Demand and Adversarial Inventory
Creators: Mengxiao Zhang - University of Iowa
Yingfei Wang - University of Washington
Haipeng Luo - University of Southern California
Resource Type: Preprint
Publication Details: arXiv
DOI: 10.48550/arxiv.2609.32949
ISSN: 2331-8422
Publisher: arXiv
Language: English
Date posted: 09/26/2026
Academic Unit: Business Analytics
Record Identifier: 9985241009602771

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