# Model-Free Assortment Pricing with Transaction Data

arXiv: https://arxiv.org/abs/2101.02251 · HTML: https://mlsanity.com/paper/2101.02251/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 6 Jan 2021.

## Built on by (most cited first, 6 of 6)

- [Contextual Inverse Optimization: Offline and Online Learning](https://mlsanity.com/paper/2106.14015/) (2021)
- [Loss Functions for Discrete Contextual Pricing with Observational Data](https://mlsanity.com/paper/2111.09933/) (2021)
- [Convex Surrogate Loss Functions for Contextual Pricing with Transaction Data](https://mlsanity.com/paper/2202.10944/) (2022)
- [DeepRule: An Integrated Framework for Automated Business Rule Generation via Deep Predictive Modeling and Hybrid Search Optimization](https://mlsanity.com/paper/2512.03607/) (2025)
- [LLM-Inspired Pretrain-Then-Finetune for Small-Data, Large-Scale Optimization](https://mlsanity.com/paper/2602.03690/) (2026)
- [Robust personalized pricing under uncertainty of purchase probabilities](https://mlsanity.com/paper/2407.15332/) (2024)

## Abstract (arXiv)

We study the problem when a firm sets prices for products based on the transaction data, i.e., which product past customers chose from an assortment and what were the historical prices that they observed. Our approach does not impose a model on the distribution of the customers' valuations and only assumes, instead, that purchase choices satisfy incentive-compatible constraints. The individual valuation of each past customer can then be encoded as a polyhedral set, and our approach maximizes the worst-case revenue assuming that new customers' valuations are drawn from the empirical distribution implied by the collection of such polyhedra. We show that the optimal prices in this setting can be approximated at any arbitrary precision by solving a compact mixed-integer linear program. Moreover, we study the single-product case and relate it to the traditional model-based approach. We also design three approximation strategies that are of low computational complexity and interpretable. Comprehensive numerical studies based on synthetic and real data suggest that our pricing approach is uniquely beneficial when the historical data has a limited size or is susceptible to model misspecification.