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A central object in optimal stopping theory is the single-choice prophet inequality for independent, identically distributed random variables: Given a sequence of random variables $X_1,\dots,X_n$ drawn independently from a distribution $F$,…

Data Structures and Algorithms · Computer Science 2021-04-08 José R. Correa , Paul Dütting , Felix Fischer , Kevin Schewior

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

We study adaptive data-dependent dimensionality reduction in the context of supervised learning in general metric spaces. Our main statistical contribution is a generalization bound for Lipschitz functions in metric spaces that are…

Machine Learning · Computer Science 2015-03-26 Lee-Ad Gottlieb , Aryeh Kontorovich , Robert Krauthgamer

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

In the classical prophet inequality, a gambler faces a sequence of items, whose values are drawn independently from known distributions. Upon the arrival of each item, its value is realized and the gambler either accepts it and the game…

Data Structures and Algorithms · Computer Science 2022-04-05 Bo Peng , Zhihao Gavin Tang

We consider the problem of the Zinkevich (2003)-style dynamic regret minimization in online learning with exp-concave losses. We show that whenever improper learning is allowed, a Strongly Adaptive online learner achieves the dynamic regret…

Machine Learning · Computer Science 2021-07-06 Dheeraj Baby , Yu-Xiang Wang

We study an optimal stopping problem under non-exponential discounting, where the state process is a multi-dimensional continuous strong Markov process. The discount function is taken to be log sub-additive, capturing decreasing impatience…

Mathematical Finance · Quantitative Finance 2021-07-14 Yu-Jui Huang , Zhenhua 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

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

Solving optimal stopping problems by backward induction in high dimensions is often very complex since the computation of conditional expectations is required. Typically, such computations are based on regression, a method that suffers from…

Probability · Mathematics 2022-05-19 Martin Redmann

For dynamical systems that switch between different modes of operation, parameter variation can cause periodic solutions to lose or acquire new switching events. When this causes the eigenvalues (stability multipliers) associated with the…

Dynamical Systems · Mathematics 2024-12-17 David J. W. Simpson

We consider prophet inequalities under downward-closed constraints. In this problem, a decision-maker makes immediate and irrevocable choices on arriving elements, subject to constraints. Traditionally, performance is compared to the…

Computer Science and Game Theory · Computer Science 2023-10-10 Tomer Ezra , Stefano Leonardi , Rebecca Reiffenhäuser , Matteo Russo , Alexandros Tsigonias-Dimitriadis

Optimal stopping theory is a powerful tool for analyzing scenarios such as online auctions in which we generally require optimizing an objective function over the space of stopping rules for an allocation process under uncertainty. Perhaps…

Computer Science and Game Theory · Computer Science 2015-10-16 Hossein Esfandiari , MohammadTaghi Hajiaghayi , Vahid Liaghat , Morteza Monemizadeh

This paper studies classification with an abstention option in the online setting. In this setting, examples arrive sequentially, the learner is given a hypothesis class $\mathcal H$, and the goal of the learner is to either predict a label…

Machine Learning · Computer Science 2016-09-29 Chicheng Zhang , Kamalika Chaudhuri

We introduce the problem of $k$-chasing of convex functions, a simultaneous generalization of both the famous k-server problem in $R^d$, and of the problem of chasing convex bodies and functions. Aside from fundamental interest in this…

Data Structures and Algorithms · Computer Science 2020-04-17 Sébastien Bubeck , Yuval Rabani , Mark Sellke

Quantum resources can improve communication complexity problems (CCPs) beyond their classical constraints. One quantum approach is to share entanglement and create correlations violating a Bell inequality, which can then assist classical…

We consider a combinatorial auction setting where buyers have fractionally subadditive (XOS) valuations over the items and the seller's objective is to maximize the social welfare. A prophet inequality in this setting bounds the competitive…

Computer Science and Game Theory · Computer Science 2025-05-23 Shuchi Chawla , Trung Dang , Zhiyi Huang , Yifan Wang

We consider the problem of constructing probabilistic predictions that lead to accurate decisions when employed by downstream users to inform actions. For a single decision maker, designing an optimal predictor is equivalent to minimizing a…

Machine Learning · Computer Science 2025-10-15 Isaac Gibbs , Ryan J. Tibshirani

We study the framework of universal dynamic regret minimization with strongly convex losses. We answer an open problem in Baby and Wang 2021 by showing that in a proper learning setup, Strongly Adaptive algorithms can achieve the near…

Machine Learning · Computer Science 2022-01-25 Dheeraj Baby , Yu-Xiang Wang

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