Omar Mouchtaki

Achraf Bahamou, Omar Besbes, Omar Mouchtaki

Problem definition: We study a data-driven pricing problem in which a seller sets a price for a single item based on demand observed at a limited number of historical prices. Our goal is to quantify the value of such information and to guide efficient price experimentation under practical constraints. Methodology/results: Our main methodological contribution is an exact reduction that characterizes the maximin revenue ratio, defined as the worst-case revenue achievable using only past data relative to the optimal revenue under full information. This reduction transforms an infinite-dimensional problem into a tractable one-dimensional optimization problem, allowing us to compute near-optimal pricing policies with explicit guarantees and to precisely quantify the value of historical data. Managerial implications: Motivated by practical constraints that limit price changes, we first evaluate the value of local information and show that the sign of the revenue gradient at a single price can provide significant guidance. We then use our framework to design efficient price experiments: we develop a method to select the next price to test so as to maximize future robust performance, and show how to substantially reduce the number of experiments needed to achieve target revenue guarantees in dynamic pricing. Finally, we show that our approach remains effective with noisy demand data, achieving near-optimal performance with as few as 25 to 100 samples per price.

Omar Besbes, Will Ma, Omar Mouchtaki

How should one leverage historical data when past observations are not perfectly indicative of the future, e.g., due to the presence of unobserved confounders which one cannot "correct" for? Motivated by this question, we study a data-driven decision-making framework in which historical samples are generated from unknown and different distributions assumed to lie in a heterogeneity ball with known radius and centered around the (also) unknown future (out-of-sample) distribution on which the performance of a decision will be evaluated. This work aims at analyzing the performance of central data-driven policies but also near-optimal ones in these heterogeneous environments and understanding key drivers of performance. We establish a first result which allows to upper bound the asymptotic worst-case regret of a broad class of policies. Leveraging this result, for any integral probability metric, we provide a general analysis of the performance achieved by Sample Average Approximation (SAA) as a function of the radius of the heterogeneity ball. This analysis is centered around the approximation parameter, a notion of complexity we introduce to capture how the interplay between the heterogeneity and the problem structure impacts the performance of SAA. In turn, we illustrate through several widely-studied problems -- e.g., newsvendor, pricing -- how this methodology can be applied and find that the performance of SAA varies considerably depending on the combinations of problem classes and heterogeneity. The failure of SAA for certain instances motivates the design of alternative policies to achieve rate-optimality. We derive problem-dependent policies achieving strong guarantees for the illustrative problems described above and provide initial results towards a principled approach for the design and analysis of general rate-optimal algorithms.

Omar Besbes, Will Ma, Omar Mouchtaki

In this work, we study how the relevance/quality and quantity of past data influence performance by analyzing a contextual Newsvendor problem, in which a decision-maker trades off between underage and overage costs under uncertain demand. We consider a setting in which past demands observed under ``close by'' contexts come from close by distributions and analyze the performance of data-driven algorithms through a notion of context-dependent worst-case expected regret. We analyze the broad class of Weighted Empirical Risk Minimization (WERM) policies which weigh past data according to their similarity in the contextual space. This class includes classical policies such as ERM, k-Nearest Neighbors and kernel-based policies. Our main methodological contribution is to characterize exactly the worst-case regret of any WERM policy on any given configuration of contexts. To the best of our knowledge, this provides the first understanding of tight performance guarantees in any contextual decision-making problem, with past literature focusing on upper bounds via concentration inequalities. We instead take an optimization approach, and isolate a structure in the Newsvendor loss function that allows to reduce the infinite-dimensional optimization problem over worst-case distributions to a simple line search. This in turn allows us to unveil fundamental insights that were obfuscated by previous general-purpose bounds. We characterize actual guaranteed performance as a function of the contexts, as well as granular insights on the learning curve of algorithms.

Rachitesh Kumar, Omar Mouchtaki

We study the offline data-driven newsvendor problem with censored demand data. In contrast to prior works where demand is fully observed, we consider the setting where demand is censored at the inventory level and only sales are observed; sales match demand when there is sufficient inventory, and equal the available inventory otherwise. We provide a general procedure to compute the exact worst-case regret of classical data-driven inventory policies, evaluated over all demand distributions. Our main technical result shows that this infinite-dimensional, non-convex optimization problem can be reduced to a finite-dimensional one, enabling an exact characterization of the performance of policies for any sample size and censoring levels. We leverage this reduction to derive sharp insights on the achievable performance of standard inventory policies under demand censoring. In particular, our analysis of the Kaplan-Meier policy shows that while demand censoring fundamentally limits what can be learned from passive sales data, just a small amount of targeted exploration at high inventory levels can substantially improve worst-case guarantees, enabling near-optimal performance even under heavy censoring. In contrast, when the point-of-sale system does not record stockout events and only reports realized sales, a natural and commonly used approach is to treat sales as demand. Our results show that policies based on this sales-as-demand heuristic can suffer severe performance degradation as censored data accumulates, highlighting how the quality of point-of-sale information critically shapes what can, and cannot, be learned offline.

Ilan Lobel, Humberto Moreira, Omar Mouchtaki

We investigate a Bayesian mechanism design problem where a seller seeks to maximize revenue by selling an indivisible good to one of n buyers, incorporating potentially unreliable predictions (signals) of buyers' private values derived from a machine learning model. We propose a framework where these signals are sometimes reflective of buyers' true valuations but other times are hallucinations, which are uncorrelated with the buyers' true valuations. Our main contribution is a characterization of the optimal auction under this framework. Our characterization establishes a near-decomposition of how to treat types above and below the signal. For the one buyer case, the seller's optimal strategy is to post one of three fairly intuitive prices depending on the signal, which we call the "ignore", "follow" and "cap" actions.