Omar Besbes

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.

Amine Allouah, Omar Besbes, Josué D Figueroa et al.

Online marketplaces will be transformed by autonomous AI agents acting on behalf of consumers. Rather than humans browsing and clicking, AI agents can parse webpages or interact through APIs to evaluate products, and transact. This raises a fundamental question: what do AI agents buy-and why? We develop ACES, a sandbox environment that pairs a platform-agnostic agent with a fully programmable mock marketplace to study this. We first explore aggregate choices, revealing that modal choices can differ across models, with AI agents sometimes concentrating on a few products, raising competition questions. We then analyze the drivers of choices through rationality checks and randomized experiments on product positions and listing attributes. Models show sizeable and heterogeneous position effects: all favor the top row, yet different models prefer different columns, undermining the assumption of a universal ``top'' rank. They penalize sponsored tags, reward endorsements, and sensitivities to price, ratings, and reviews are directionally as expected, but vary sharply across models. Finally, we find that a seller-side agent that makes minor tweaks to product descriptions can deliver substantial market-share gains by targeting AI buyer preferences. Our findings reveal how AI agents behave in e-commerce, and surface concrete seller strategy, platform design, and regulatory questions.

Omar Besbes, Yuri Fonseca, Ilan Lobel

We study the problems of offline and online contextual optimization with feedback information, where instead of observing the loss, we observe, after-the-fact, the optimal action an oracle with full knowledge of the objective function would have taken. We aim to minimize regret, which is defined as the difference between our losses and the ones incurred by an all-knowing oracle. In the offline setting, the decision-maker has information available from past periods and needs to make one decision, while in the online setting, the decision-maker optimizes decisions dynamically over time based a new set of feasible actions and contextual functions in each period. For the offline setting, we characterize the optimal minimax policy, establishing the performance that can be achieved as a function of the underlying geometry of the information induced by the data. In the online setting, we leverage this geometric characterization to optimize the cumulative regret. We develop an algorithm that yields the first regret bound for this problem that is logarithmic in the time horizon. Finally, we show via simulation that our proposed algorithms outperform previous methods from the literature.

Omar Besbes, Yonatan Gur, Assaf Zeevi

In a multi-armed bandit (MAB) problem a gambler needs to choose at each round of play one of K arms, each characterized by an unknown reward distribution. Reward realizations are only observed when an arm is selected, and the gambler's objective is to maximize his cumulative expected earnings over some given horizon of play T. To do this, the gambler needs to acquire information about arms (exploration) while simultaneously optimizing immediate rewards (exploitation); the price paid due to this trade off is often referred to as the regret, and the main question is how small can this price be as a function of the horizon length T. This problem has been studied extensively when the reward distributions do not change over time; an assumption that supports a sharp characterization of the regret, yet is often violated in practical settings. In this paper, we focus on a MAB formulation which allows for a broad range of temporal uncertainties in the rewards, while still maintaining mathematical tractability. We fully characterize the (regret) complexity of this class of MAB problems by establishing a direct link between the extent of allowable reward "variation" and the minimal achievable regret. Our analysis draws some connections between two rather disparate strands of literature: the adversarial and the stochastic MAB frameworks.