Minimax-Optimal Semiparametric Contextual Dynamic Pricing with Multimodal Revenue

• URL: http://arxiv.org/abs/2608.03142v1
• Date: Tue, 04 Aug 2026 05:14:26 GMT
• Title: Minimax-Optimal Semiparametric Contextual Dynamic Pricing with Multimodal Revenue
• Abstract summary: We study contextual dynamic pricing withBounded, possibly nonbinary purchase quantities.<n>We impose neither concavity nor strongmodality on revenue and allow uniunique optimal prices.
• Score: 6.201103695201767
• License: http://creativecommons.org/licenses/by/4.0/
• 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 Hölder-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.

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