# Minimax Optimality in Contextual Dynamic Pricing with General Valuation Models

arXiv: https://arxiv.org/abs/2406.17184 · HTML: https://mlsanity.com/paper/2406.17184/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 24 references that are in the map.
- First posted on arXiv 24 Jun 2024.

## Builds on (most cited first, 10 of 10)

- [Beyond UCB: Optimal and Efficient Contextual Bandits with Regression Oracles](https://mlsanity.com/paper/2002.04926/) (2020)
- [Dynamic Pricing in High-dimensions](https://mlsanity.com/paper/1609.07574/) (2016)
- [Nearly Minimax-Optimal Regret for Linearly Parameterized Bandits](https://mlsanity.com/paper/1904.00242/) (2019)
- [Sparsity-Agnostic Lasso Bandit](https://mlsanity.com/paper/2007.08477/) (2020)
- [Dynamic Incentive-aware Learning: Robust Pricing in Contextual Auctions](https://mlsanity.com/paper/2002.11137/) (2020)
- [Dynamic Pricing with Finitely Many Unknown Valuations](https://mlsanity.com/paper/1807.03288/) (2018)
- [Policy Optimization Using Semi-parametric Models for Dynamic Pricing](https://mlsanity.com/paper/2109.06368/) (2021)
- [Distribution-free Contextual Dynamic Pricing](https://mlsanity.com/paper/2109.07340/) (2021)
- [Towards Agnostic Feature-based Dynamic Pricing: Linear Policies vs Linear Valuation with Unknown Noise](https://mlsanity.com/paper/2201.11341/) (2022)
- [Dynamic Contextual Pricing with Doubly Non-Parametric Random Utility Models](https://mlsanity.com/paper/2405.06866/) (2024)

## Built on by (most cited first, 2 of 2)

- [Optimal Contextual Pricing under Agnostic Non-Lipschitz Demand](https://mlsanity.com/paper/2605.05609/) (2026)
- [Learning to Price and Stock Under Contextual and Censored Demand](https://mlsanity.com/paper/2609.06083/) (2026)

## Abstract (arXiv)

We study contextual dynamic pricing, where a decision maker posts personalized prices based on observable contexts and receives binary purchase feedback indicating whether the customer's valuation exceeds the price. Each valuation is modeled as an unknown latent function of the context, corrupted by independent and identically distributed market noise from an unknown distribution. Relying only on Lipschitz continuity of the noise distribution and bounded valuations, we propose a minimax-optimal algorithm. To accommodate the unknown distribution, our method discretizes the relevant noise range to form a finite set of candidate prices, then applies layered data partitioning to obtain confidence bounds substantially tighter than those derived via the elliptical-potential lemma. A key advantage is that estimation bias in the valuation function cancels when comparing upper confidence bounds, eliminating the need to know the Lipschitz constant. The framework extends beyond linear models to general function classes through offline regression oracles. Our regret analysis depends solely on the oracle's estimation error, typically governed by the statistical complexity of the class. These techniques yield a regret upper bound matching the minimax lower bound up to logarithmic factors. Furthermore, we refine these guarantees under additional structures -- e.g., linear valuation models, second-order smoothness, sparsity, and known noise distribution or observable valuations -- and compare our bounds and assumptions with prior dynamic-pricing methods. Finally, numerical experiments corroborate the theory and show clear improvements over benchmark methods.