Minimax-Optimal Semiparametric Contextual Dynamic Pricing with Multimodal Revenue

[Submitted on 4 Aug 2026]

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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.

Submission history

From: Xueping Gong [view email]
[v1] Tue, 4 Aug 2026 05:14:26 UTC (227 KB)