English
Related papers

Related papers: A combinatorial proof for the secretary problem wi…

200 papers

The secretary problem is a classic model for online decision making. Recently, combinatorial extensions such as matroid or matching secretary problems have become an important tool to study algorithmic problems in dynamic markets. Here the…

Data Structures and Algorithms · Computer Science 2017-08-28 Martin Hoefer , Bojana Kodric

We study variants of the secretary problem, where $N$, the number of candidates, is a random variable, and the decision maker wants to maximize the probability of success -- picking the largest number among the $N$ candidates -- using only…

Data Structures and Algorithms · Computer Science 2023-10-13 Junhui Zhang , Patrick Jaillet

We study a learning-augmented variant of the secretary problem, recently introduced by Fujii and Yoshida (2023), in which the decision-maker has access to machine-learned predictions of candidate values. The central challenge is to balance…

Data Structures and Algorithms · Computer Science 2026-01-13 Helia Karisani , Mohammadreza Daneshvaramoli , Hedyeh Beyhaghi , Mohammad Hajiesmaili , Cameron Musco

We take a unifying approach to single selection optimal stopping problems with random arrival order and independent sampling of items. In the problem we consider, a decision maker (DM) initially gets to sample each of $N$ items…

Computer Science and Game Theory · Computer Science 2021-08-11 José Correa , Andrés Cristi , Boris Epstein , José Soto

This paper introduces a heuristic framework for the Best Secretary Problem, where one item must be selected using rank information only. We develop five data-responsive rules extending classical fixed-cutoff methods: an expected-record…

Applications · Statistics 2025-11-14 Eugene Seong

We consider two variants of the secretary problem, the\emph{ Best-or-Worst} and the \emph{Postdoc} problems, which are closely related. First, we prove that both variants, in their standard form with binary payoff 1 or 0, share the same…

Probability · Mathematics 2017-06-23 L. Bayon , P. Fortuny Ayuso , J. M. Grau , A. M. Oller-Marcen , M. M. Ruiz

We consider a variant of the secretary problem in which the candidates state their expected salary at the interview, which we assume is in accordance with their qualifications. The goal is for the employer to hire the best or the worst…

Probability · Mathematics 2016-03-22 L. Bayon , J. Grau , A. M. Oller-Marcen , M. Ruiz , P. M. Suarez

The game of best choice, also known as the secretary problem, is a model for sequential decision making with many variations in the literature. Notably, the classical setup assumes that the sequence of candidate rankings is uniformly…

Combinatorics · Mathematics 2019-03-13 Madeline Crews , Brant Jones , Kaitlyn Myers , Laura Taalman , Michael Urbanski , Breeann Wilson

A version of the classical secretary problem is studied, in which one is interested in selecting one of the b best out of a group of n differently ranked persons who are presented one by one in a random order. It is assumed that b is a…

Probability · Mathematics 2010-09-06 Chris Dietz , Dinard van der Laan , Ad Ridder

In the classical secretary problem, one attempts to find the maximum of an unknown and unlearnable distribution through sequential search. In many real-world searches, however, distributions are not entirely unknown and can be learned…

Computer Science and Game Theory · Computer Science 2017-08-30 Daniel G. Goldstein , R. Preston McAfee , Siddharth Suri , James R. Wright

The secretary problem is probably the purest model of decision making under uncertainty. In this paper we ask which advice can we give the algorithm to improve its success probability? We propose a general model that unifies a broad range…

Data Structures and Algorithms · Computer Science 2020-11-16 Paul Dütting , Silvio Lattanzi , Renato Paes Leme , Sergei Vassilvitskii

In this paper we consider the so-called Multi-returning secretary problem, a version of the Secretary problem in which each candidate has $m$ identical copies. The case $m=2$ has already been completely solved by several authors using…

Probability · Mathematics 2020-10-16 L. Bayon , P. Fortuny , J. M. Grau , A. Oller Marcen , M. M. Ruiz

In the online random-arrival model, an algorithm receives a sequence of n requests that arrive in a random order. The algorithm is expected to make an irrevocable decision with regard to each request based only on the observed history. We…

Data Structures and Algorithms · Computer Science 2014-07-08 Shai Vardi

This article considers a problem arising from a two-player game based on the classical secretary problem. First, Player 1 selects one object from a sequence as in the secretary problem. All of the other objects are then presented to Player…

Computer Science and Game Theory · Computer Science 2024-09-09 David Ramsey

We study secretary problems in settings with multiple agents. In the standard secretary problem, a sequence of arbitrary awards arrive online, in a random order, and a single decision maker makes an immediate and irrevocable decision…

Computer Science and Game Theory · Computer Science 2020-07-15 Tomer Ezra , Michal Feldman , Ron Kupfer

Suppose that $n$ items arrive online in random order and the goal is to select $k$ of them such that the expected sum of the selected items is maximized. The decision for any item is irrevocable and must be made on arrival without knowing…

Data Structures and Algorithms · Computer Science 2020-12-02 Susanne Albers , Leon Ladewig

In the classical secretary problem, $n$ ranked items arrive one by one, and each item's rank relative to its predecessors is noted. The observer must select or reject each item as it arrives, with the object of selecting the item of highest…

Probability · Mathematics 2023-07-21 Ross G. Pinsky , Tomer Zilca

In the secretary problem we are faced with an online sequence of elements with values. Upon seeing an element we have to make an irrevocable take-it-or-leave-it decision. The goal is to maximize the probability of picking the element of…

Computer Science and Game Theory · Computer Science 2020-11-17 José Correa , Andrés Cristi , Laurent Feuilloley , Tim Oosterwijk , Alexandros Tsigonias-Dimitriadis

In learning-augmented online algorithms, predictions are usually valued for what they say: a value estimate, a solution, or an algorithmic recommendation. This paper shows that predictions can also be valuable solely due to their arrival…

Data Structures and Algorithms · Computer Science 2026-05-22 Franziska Eberle , Alexander Lindermayr

In this paper we consider two variants of the Secretary problem: The Best-or-Worst and the Postdoc problems. We extend previous work by considering that the number of objects is not known and follows either a discrete Uniform distribution…

Probability · Mathematics 2018-11-13 L. Bayon , P. Fortuny , J. M. Grau , M. M Ruiz , M. A. Oller-Marcen