# Minimax-Optimal Semiparametric Contextual Dynamic Pricing with Multimodal Revenue

arXiv: https://arxiv.org/abs/2608.03142 · HTML: https://mlsanity.com/paper/2608.03142/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 4 of its 29 references that are in the map.
- First posted on arXiv 4 Aug 2026.

## Builds on (most cited first, 4 of 4)

- [Dynamic Contextual Pricing with Doubly Non-Parametric Random Utility Models](https://mlsanity.com/paper/2405.06866/) (2024)
- [Optimal Contextual Pricing under Agnostic Non-Lipschitz Demand](https://mlsanity.com/paper/2605.05609/) (2026)
- [Optimal Semiparametric Dynamic Pricing with Feature Diversity](https://mlsanity.com/paper/2605.04207/) (2026)
- [Harnessing Unimodality in Semiparametric Contextual Pricing via Oracle Price Map Learning](https://mlsanity.com/paper/2605.15411/) (2026)

## Abstract (arXiv)

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.