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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…
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…
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…
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 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…
In this paper, we investigate two variants of the secretary problem. In these variants, we are presented with a sequence of numbers $X_i$ that come from distributions $\mathcal{D}_i$, and that arrive in either random or adversarial order.…
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…
We consider two variations of the classical secretary problem. * A variation of the returning secretary problem where each interviewee may appear a second time with a fixed probability p. The decision-maker observes interviewees…
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 a generalization of the secretary problem, where decisions do not have to be made immediately upon candidates' arrivals. After arriving, each candidate stays in the system for some (random) amount of time and then leaves, whereupon…
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…
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…
Candidates arrive sequentially for an interview process which results in them being ranked relative to their predecessors. Based on the ranks available at each time, one must develop a decision mechanism that selects or dismisses the…
As a famous result, the ``37\% Law'' for Secretary Problem has widely influenced peoples' perception on online decision strategies about choice. However, using this strategy, too many attractive candidates may be rejected in the first 37\%,…
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…
A version of the secretary problem called the duration problem, in which the objective is to maximize the time of possession of relatively best objects or the second best, is treated. It is shown that in this duration problem there are…
We extend the standard online worst-case model to accommodate past experience which is available to the online player in many practical scenarios. We do this by revealing a random sample of the adversarial input to the online player ahead…
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…
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 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…