Personalized prices can boost revenue, but they increasingly draw fire for hidden discrimination. A new study, “Dynamic Pricing with Fairness Constraints,” by Maxime C. Cohen, Sentao Miao, and Yining Wang, shows that firms can learn demand while staying fair at the same time. The authors embed two complementary notions of fairness into the classic learning-and-earning problem. The first, price fairness, limits price gaps across customer groups and over time, whereas the second, demand fairness, keeps realized demand shares balanced. To enforce price fairness, the authors design FaPU, an infrequently updated upper confidence bound algorithm that respects both group and temporal limits while securing near-optimal regret and matching lower bounds. For demand fairness, they propose FaPD, a primal-dual learner that meets aggregate demand quotas with high probability and the same near-optimal regret rate. Beyond providing tight theoretical analyses, the paper quantifies the “price of fairness” and outlines extensions to non-stationary markets, offering regulators and practitioners evidence that equity and profitability can coexist in algorithmic pricing.

A Review of Inverse Optimization In recent years, there has been an explosion of interest in the mathematics and applications of inverse optimization. Unlike traditional optimization, which seeks to compute optimal decisions given an objective and constraints, inverse optimization takes decisions as input and determines an objective and/or constraints that render these decisions approximately or exactly optimal. In “Inverse Optimization: Theory and Applications,” Chan, Rafid, and Zhu provide a comprehensive review of both the methodological and application-oriented literature. Specifically, the authors consolidate various model properties, reformulation techniques, and computational methods of different classes of inverse optimization problems. The authors also review a wide range of application areas that include, but are not limited to, transportation, logistics, healthcare, and energy systems. The paper concludes with several major directions for future research.