Minimax-Optimal Semiparametric Contextual Dynamic Pricing with Multimodal Revenue

2026-08-04

AI Summary

This study addresses contextual dynamic pricing under arbitrary covariate sequences and non-binary purchase quantities, tackling the challenges of multimodal revenue landscapes and non-unique optimal prices without assuming concavity or strong unimodality of the revenue function. The authors propose a hierarchical decision partitioning strategy that integrates directional pilot estimation, local polynomial regression, adaptive data allocation, and global action elimination, augmented by a pilot correction mechanism to eliminate the first-order bias induced by estimation errors in valuation parameters. Under a semiparametric surplus index model with Hölder-smooth response functions, the method achieves, up to logarithmic factors, the smoothness-dependent minimax optimal convergence rate. The bound is shown to be tight in the special case of constant contexts and binary demand, establishing the first minimax optimal theoretical guarantee for such a general setting.

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.

Problem

• contextual dynamic pricing
• semiparametric model
• nonparametric revenue
• minimax optimality
• adaptive pricing

Innovation

• semiparametric contextual dynamic pricing
• minimax optimality
• pilot-corrected estimation
• adaptive sampling
• Hölder-smooth response