# Robust personalized pricing under uncertainty of purchase probabilities

arXiv: https://arxiv.org/abs/2407.15332 · HTML: https://mlsanity.com/paper/2407.15332/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 15 of its 48 references that are in the map.
- First posted on arXiv 22 Jul 2024.

## Builds on (most cited first, 15 of 15)

- [Recursive Partitioning for Heterogeneous Causal Effects](https://mlsanity.com/paper/1504.01132/) (2015)
- [Statistics of Robust Optimization: A Generalized Empirical Likelihood Approach](https://mlsanity.com/paper/1610.03425/) (2016)
- [Recursive Partitioning for Personalization using Observational Data](https://mlsanity.com/paper/1608.08925/) (2016)
- [Model Distillation for Revenue Optimization: Interpretable Personalized Pricing](https://mlsanity.com/paper/2007.01903/) (2020)
- [Optimal Policy Trees](https://mlsanity.com/paper/2012.02279/) (2020)
- [Fairness, Welfare, and Equity in Personalized Pricing](https://mlsanity.com/paper/2012.11066/) (2020)
- [Bootstrap Robust Prescriptive Analytics](https://mlsanity.com/paper/1711.09974/) (2017)
- [Optimization Beyond Prediction: Prescriptive Price Optimization](https://mlsanity.com/paper/1605.05422/) (2016)
- [Model-Free Assortment Pricing with Transaction Data](https://mlsanity.com/paper/2101.02251/) (2021)
- [Constrained Prescriptive Trees via Column Generation](https://mlsanity.com/paper/2207.10163/) (2022)
- [Distributionally Robust Prescriptive Analytics with Wasserstein Distance](https://mlsanity.com/paper/2106.05724/) (2021)
- [Robust portfolio optimization model for electronic coupon allocation](https://mlsanity.com/paper/2405.12865/) (2024)
- [Price Optimization with Practical Constraints](https://mlsanity.com/paper/2104.09597/) (2021)
- [Interpretable Price Bounds Estimation with Shape Constraints in Price Optimization](https://mlsanity.com/paper/2405.14909/) (2024)
- [Robust portfolio optimization for recommender systems considering uncertainty of estimated statistics](https://mlsanity.com/paper/2406.10250/) (2024)

## Abstract (arXiv)

This paper is concerned with personalized pricing models aimed at maximizing the expected revenues or profits for a single item. While it is essential for personalized pricing to predict the purchase probabilities for each consumer, these predicted values are inherently subject to unavoidable errors that can negatively impact the realized revenues and profits. To address this issue, we focus on robust optimization techniques that yield reliable solutions to optimization problems under uncertainty. Specifically, we propose a robust optimization model for personalized pricing that accounts for the uncertainty of predicted purchase probabilities. This model can be formulated as a mixed-integer linear optimization problem, which can be solved exactly using mathematical optimization solvers. We also develop a Lagrangian decomposition algorithm combined with line search to efficiently find high-quality solutions for large-scale optimization problems. Experimental results demonstrate the effectiveness of our robust optimization model and highlight the utility of our Lagrangian decomposition algorithm in terms of both computational efficiency and solution quality.