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This paper investigates contextual dynamic pricing using a semiparametric surplus-index model, accommodating arbitrary covariate sequences and bounded purchase quantities. The authors introduce a pilot-corrected layered decision-partitioning policy that effectively mitigates valuation-parameter error while leveraging local polynomial learning and adaptive sampling. The proposed method achieves a minimax smoothness-dependent horizon rate, demonstrating optimal performance even in scenarios with nonunique optimal prices and without imposing strict revenue constraints.
Achieving minimax optimality in dynamic pricing without the need for strict revenue concavity opens new avenues for pricing strategies in complex market environments.
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.
