Minimax-Optimal Semiparametric Contextual Dynamic Pricing with Multimodal Revenue
Xueping Gong, Zhuoluo Zhang, Zhaowei Miao, Jiheng Zhang
stat.ML, cs.AI, cs.LG
Submitted: 2026-08-04
Comments: 53 pages
License: http://creativecommons.org/licenses/by/4.0/
The gist: We study contextual dynamic pricing with arbitrary covariate sequences and bounded, possibly nonbinary purchase quantities.
Terminology
Abstract
We study contextual dynamic pricing with arbitrary covariate sequences and bounded, possibly nonbinary purchase quantities. Demand follows a semiparametric surplus-index model with an unknown linear valuation parameter and an unknown H"older-smooth response. We impose neither concavity nor strong unimodality on revenue and allow nonunique optimal prices. We develop a pilot-corrected layered decision-partitioning policy that combines directional pilot estimation, local polynomial learning, predictable data assignment, and global action elimination. Pilot correction removes the first-order effect of valuation-parameter error, while permanent labels enable concentration under adaptive sampling. The policy attains the minimax smoothness-dependent horizon rate up to logarithmic factors; a matching lower bound already holds for a constant-context binary-demand subclass.
Sources
- Optimal Semiparametric Dynamic Pricing with Feature Diversity
- Dynamic Contextual Pricing with Doubly Non-Parametric Random Utility Models
- Harnessing Unimodality in Semiparametric Contextual Pricing via Oracle Price Map Learning
- Optimal Contextual Pricing under Agnostic Non-Lipschitz Demand
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