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Related papers: Prophet Inequalities over Time

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In the classic prophet inequality, samples from independent random variables arrive online. A gambler that knows the distributions must decide at each point in time whether to stop and pick the current sample or to continue and lose that…

Data Structures and Algorithms · Computer Science 2019-03-13 Jose Correa , Raimundo Saona , Bruno Ziliotto

We study the prophet inequality, a fundamental problem in online decision-making and optimal stopping, in a practical setting where rewards are observed only through noisy realizations and reward distributions are unknown. At each stage,…

Machine Learning · Statistics 2026-04-03 Jung-hun Kim , Vianney Perchet

We consider the prophet inequality problem for (not necessarily bipartite) matching problems with independent edge values, under both edge arrivals and vertex arrivals. We show constant-factor prophet inequalities for the case where the…

Data Structures and Algorithms · Computer Science 2021-08-03 Paul Dütting , Federico Fusco , Philip Lazos , Stefano Leonardi , Rebecca Reiffenhäuser

Consider a gambler who observes a sequence of independent, non-negative random numbers and is allowed to stop the sequence at any time, claiming a reward equal to the most recent observation. The famous prophet inequality of Krengel,…

Data Structures and Algorithms · Computer Science 2012-01-24 Robert Kleinberg , S. Matthew Weinberg

We study the i.i.d. $k$-selection prophet inequality problem, where a decision-maker sequentially observes $n$ independent nonnegative rewards and may accept at most $k$ of them without knowledge of future realizations. The objective is to…

Optimization and Control · Mathematics 2026-02-24 Jieming Kong , Karthyek Murthy

We study threshold testing, an elementary probing model with the goal to choose a large value out of $n$ i.i.d. random variables. An algorithm can test each variable $X_i$ once for some threshold $t_i$, and the test returns binary feedback…

Data Structures and Algorithms · Computer Science 2024-06-13 Martin Hoefer , Kevin Schewior

Prophet inequalities bound the expected reward that can be obtained in a stopping problem by the optimal reward of its corresponding off-line version. We propose a systematic technique for deriving prophet inequalities for stopping problems…

Theoretical Economics · Economics 2026-02-10 Halil I. Bayrak , Mustafa Ç. Pınar , Rakesh Vohra

We study the classic single-choice prophet inequality problem through a resource augmentation lens. Our goal is to bound the $(1-\varepsilon)$-competition complexity of different types of online algorithms. This metric asks for the smallest…

Computer Science and Game Theory · Computer Science 2024-02-23 Johannes Brustle , José Correa , Paul Dütting , Tomer Ezra , Michal Feldman , Victor Verdugo

We explore a prophet inequality problem, where the values of a sequence of items are drawn i.i.d. from some distribution, and an online decision maker must select one item irrevocably. We establish that $\mathrm{CR}_{\ell}$ the worst-case…

Data Structures and Algorithms · Computer Science 2025-01-13 Mathieu Molina , Nicolas Gast , Patrick Loiseau , Vianney Perchet

This paper considers a finite horizon optimal stopping problem for a sequence of independent and identically distributed random variables, where the objective is to design stopping rules that attempt to select the random variable with the…

Probability · Mathematics 2026-05-20 Alexander Goldenshluger , Yaakov Malinovsky , Assaf Zeevi

We study the prophet secretary problem, a well-studied variant of the classic prophet inequality, where values are drawn from independent known distributions but arrive in uniformly random order. Upon seeing a value at each step, the…

Computer Science and Game Theory · Computer Science 2023-05-19 Paul Dütting , Evangelia Gergatsouli , Rojin Rezvan , Yifeng Teng , Alexandros Tsigonias-Dimitriadis

We introduce a model of competing agents in a prophet setting, where rewards arrive online, and decisions are made immediately and irrevocably. The rewards are unknown from the outset, but they are drawn from a known probability…

Computer Science and Game Theory · Computer Science 2021-07-02 Tomer Ezra , Michal Feldman , Ron Kupfer

Prophet inequality concerns a basic optimal stopping problem and states that simple threshold stopping policies -- i.e., accepting the first reward larger than a certain threshold -- can achieve tight $\frac{1}{2}$-approximation to the…

Computer Science and Game Theory · Computer Science 2024-10-31 Wei Tang , Haifeng Xu , Ruimin Zhang , Derek Zhu

In a classical online decision problem, a decision-maker who is trying to maximize her value inspects a sequence of arriving items to learn their values (drawn from known distributions), and decides when to stop the process by taking the…

Data Structures and Algorithms · Computer Science 2020-05-26 Nicole Immorlica , Sahil Singla , Bo Waggoner

The setting of the classic prophet inequality is as follows: a gambler is shown the probability distributions of $n$ independent, non-negative random variables with finite expectations. In their indexed order, a value is drawn from each…

Data Structures and Algorithms · Computer Science 2018-12-31 Jack Wang

Free order prophet inequalities bound the ratio between the expected value obtained by two parties each selecting a value from a set of independent random variables: a "prophet" who knows the value of each variable and may select the…

Data Structures and Algorithms · Computer Science 2020-10-20 Makis Arsenis , Odysseas Drosis , Robert Kleinberg

Prophet inequalities are a central object of study in optimal stopping theory. In the iid model, a gambler sees values in an online fashion, sampled independently from a given distribution. Upon observing each value, the gambler either…

Data Structures and Algorithms · Computer Science 2025-06-23 Giordano Giambartolomei , Frederik Mallmann-Trenn , Raimundo Saona

We initiate the study of the prophet inequality problem through the resource augmentation framework in scenarios when the values of the rewards are correlated. Our goal is to determine the number of additional rewards an online algorithm…

Machine Learning · Computer Science 2024-09-12 Tomer Ezra , Tamar Garbuz

We introduce a variant of the classic prophet inequality, called \emph{residual prophet inequality} (RPI). In the RPI problem, we consider a finite sequence of $n$ nonnegative independent random values with known distributions, and a known…

Data Structures and Algorithms · Computer Science 2025-07-24 Jose Correa , Sebastian Perez-Salazar , Dana Pizarro , Bruno Ziliotto

In online sales, sellers usually offer each potential buyer a posted price in a take-it-or-leave fashion. Buyers can sometimes see posted prices faced by other buyers, and changing the price frequently could be considered unfair. The…

Computer Science and Game Theory · Computer Science 2023-08-15 Sebastian Perez-Salazar , Mohit Singh , Alejandro Toriello