# Nonparametric Contextual Pricing and Inventory Learning under Censored Demand

arXiv: https://arxiv.org/abs/2608.30944 · HTML: https://mlsanity.com/paper/2608.30944/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 11 of its 39 references that are in the map.
- First posted on arXiv 31 Aug 2026.

## Builds on (most cited first, 11 of 11)

- [Dynamic Pricing in High-dimensions](https://mlsanity.com/paper/1609.07574/) (2016)
- [Contextual Bandits with Continuous Actions: Smoothing, Zooming, and Adapting](https://mlsanity.com/paper/1902.01520/) (2019)
- [Dynamic Pricing with Demand Covariates](https://mlsanity.com/paper/1604.07463/) (2016)
- [Nonparametric Stochastic Contextual Bandits](https://mlsanity.com/paper/1801.01750/) (2018)
- [The K-Nearest Neighbour UCB algorithm for multi-armed bandits with covariates](https://mlsanity.com/paper/1803.00316/) (2018)
- [Smoothness-Adaptive Contextual Bandits](https://mlsanity.com/paper/1910.09714/) (2019)
- [Censored Semi-Bandits: A Framework for Resource Allocation with Censored Feedback](https://mlsanity.com/paper/1909.01504/) (2019)
- [Online Estimation via Offline Estimation: An Information-Theoretic Framework](https://mlsanity.com/paper/2404.10122/) (2024)
- [A Primal-dual Learning Algorithm for Personalized Dynamic Pricing with an Inventory Constraint](https://mlsanity.com/paper/1812.09234/) (2018)
- [Offline Dynamic Inventory and Pricing Strategy: Addressing Censored and Dependent Demand](https://mlsanity.com/paper/2504.09831/) (2025)
- [Direction-Aware Offline-to-Online Learning in Linear Contextual Bandits](https://mlsanity.com/paper/2604.24016/) (2026)

## Abstract (arXiv)

In online retailing, when a product sells out, a retailer often sees only the units sold, not how many customers would have bought it had inventory been available. However, the inventory level determines how much demand is revealed, and this information can influence subsequent decisions and future profits. We study an online selling problem in which, in each round, the seller observes a market context and then makes pricing and stocking decisions based on censored sales data from previous rounds. The challenge is to learn a context-dependent pricing and stocking policy without assuming a particular formula for demand or observing realized profit. To overcome this difficulty, we propose a Mean-Calibrated Kernel UCB (MCK-UCB) algorithm that turns each incomplete sales record into a reliable guide for both inventory and price decisions, using data from past rounds with similar market conditions. This design allows us to learn while serving customers, without a separate exploration phase or the need to recover all demand hidden by stockouts. We prove the minimax optimality of the proposed algorithm, with strictly faster rates when expected profit varies more smoothly with price. Comprehensive numerical experiments have been conducted to confirm the effectiveness of the proposed algorithm.