Related papers: Secretary Problem with quality-based payoff
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…
The decision-maker (DM) sequentially evaluates up to N of different, rankable options. DM must select exactly the best one at the moment of its appearance. In the process of searching, DM finds out with each applicant whether she is the…
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…
We study the secretary problem in which rank-ordered lists are generated by the Mallows model and the goal is to identify the highest-ranked candidate through a sequential interview process which does not allow rejected candidates to be…
We investigate the hiring problem where a sequence of applicants is sequentially interviewed, and a decision on whether to hire an applicant is immediately made based on the applicant's score. For the maximal and average improvement…
We study a variation of the game of best choice (also known as the secretary problem or game of googol) under an additional assumption that the ranks of interview candidates are restricted using permutation pattern-avoidance. We describe…
We revisit the problem of selecting an item from $n$ choices that appear before us in random sequential order so as to minimize the expected rank of the item selected. In particular, we examine the stopping rule where we reject the first…
In the subject of optimal stopping, the classical secretary problem is concerned with optimally selecting the best of $n$ candidates when their relative ranks are observed sequentially. This problem has been extended to optimally selecting…
In the Secretary Problem, one has to hire the best among n candidates. The candidates are interviewed, one at a time, at a random order, and one has to decide on the spot, whether to hire a candidate or continue interviewing. It is well…
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…
The secretary problem has been a focus of extensive study with a variety of extensions that offer useful insights into the theory of optimal stopping. The original solution is to set one stopping threshold that gives rise to an immediately…
The game of best choice (or "secretary problem") is a model for making an irrevocable decision among a fixed number of candidate choices that are presented sequentially in random order, one at a time. Because the classically optimal…
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…
We define a new selection problem, \emph{Selecting with History}, which extends the secretary problem to a setting with historical information. We propose a strategy for this problem and calculate its success probability in the limit of a…
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…
We consider the secretary problem through the lens of learning-augmented algorithms. As it is known that the best possible expected competitive ratio is $1/e$ in the classic setting without predictions, a natural goal is to design…
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…
The game of best choice (also known as the secretary problem) is a model for sequential decision making with a long history and many variations. The classical setup assumes that the sequence of candidate rankings are uniformly distributed.…
The classical analysis of online algorithms, due to its worst-case nature, can be quite pessimistic when the input instance at hand is far from worst-case. Often this is not an issue with machine learning approaches, which shine in…
We study a game between $N$ job applicants who incur a cost $c$ (relative to the job value) to reveal their type during interviews and an administrator who seeks to maximize the probability of hiring the best. We define a full learning…