Related papers: Weber's optimal stopping problem and generalizatio…
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…
In this paper we revisit the basic variant of the classical secretary problem. We propose a new approach in which we separate between an agent that evaluates the secretary performance and one that has to make the hiring decision. The…
The value maximization version of the secretary problem is the problem of hiring a candidate with the largest value from a randomly ordered sequence of candidates. In this work, we consider a setting where predictions of candidate values…
The Sliding Window Secretary Problem allows a window of choices to the Classical Secretary Problem, in which there is the option to choose the previous $K$ choices immediately prior to the current choice. We consider a case of this…
In the Sequential Selection Problem (SSP), immediate and irrevocable decisions need to be made as candidates randomly arrive for a job interview. Standard SSP variants, such as the well-known secretary problem, begin with an empty selection…
A Constraint Satisfaction Problem (CSP) is a computational problem where we are given variables and constraints about them; the question is whether the variables can be assigned values such that all constraints are satisfied. We give an…
The well-known secretary problem in sequential analysis and optimal stopping theory asks one to maximize the probability of finding the optimal candidate in a sequentially examined list under the constraint that accept/reject decisions are…
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…
The objective of this paper is to show that the so-called unified approach to stopping problems with unknown cardinality introduced in Bruss (1984) proves to be efficient for solving other types of best-choice problems. We show that what we…
The secretary problem is one of the fundamental problems in online decision making; a tight competitive ratio for this problem of $1/\mathrm{e} \approx 0.368$ has been known since the 1960s. Much more recently, the study of algorithms with…
There are two major models of value uncertainty in the optimal stopping literature: the secretary model, which assumes no prior knowledge, and the prophet inequality model, which assumes full information about value distributions. In…
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…
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…
We consider generalizations of the classical secretary problem, also known as the problem of optimal choice, to posets where the only information we have is the size of the poset and the number of maximal elements. We show that, given this…
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…
Given integers $1\leq k<n$, the Gusein-Zade version of a generalized secretary problem is to choose one of the $k$ best of $n$ candidates for a secretary, which are interviewing in random order. The stopping rule in the selection is based…
We consider a variant of the classical Secretary Problem. In this setting, the candidates are ranked according to some exchangeable random variable and the quest is to maximize the expected quality of the chosen aspirant. We find an upper…
This note considers a variation of the full-information secretary problem where the random variables to be observed are independent and identically distributed. Consider $X_1,\dots,X_n$ to be an independent sequence of random variables, let…
We give asymptotic lower bounds of the value for Bruss' optimal stopping problem with multiple stopping chances. It interestingly consists of the asymptotic threshold values in the optimal multiple stopping strategy. Another interesting…
Optimal stopping problems give rise to random distributions describing how many applicants the decision-maker will sample or interview before choosing one, a quantity sometimes referred to as the search time or process duration. This…