Related papers: Secretary Problems: The Power of a Single Sample
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…
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\%,…
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…
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…
The secretary and the prophet inequality problems are central to the field of Stopping Theory. Recently, there has been a lot of work in generalizing these models to multiple items because of their applications in mechanism design. The most…
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…
The last success problem is an optimal stopping problem that aims to maximize the probability of stopping on the last success in a sequence of independent $n$ Bernoulli trials. In the classical setting where complete information about the…
One way to interpret the classical secretary problem (CSP) is to consider it as a special case of the following problem. We observe $n$ independent indicator variables $I_1,I_2,\dotsc,I_n$ sequentially and we try to stop on the last…
Online advertising has motivated interest in online selection problems. Displaying ads to the right users benefits both the platform (e.g., via pay-per-click) and the advertisers (by increasing their reach). In practice, not all users click…
In this paper, we discuss a stochastic decision problem of optimally selecting the order in which to try $n$ opportunities that may yield an uncertain reward in the future. The motivation came out from pure curiosity, after an informal…
Let us call a sequence of numbers heapable if they can be sequentially inserted to form a binary tree with the heap property, where each insertion subsequent to the first occurs at a leaf of the tree, i.e. below a previously placed number.…
This paper studies an online trading variant of the classical secretary problem, called secretary problem variant trading (SPVT), from the perspective of an intermediary who facilitates trade between a seller and $n$ buyers (collectively…
In the prophet secretary problem, $n$ values are drawn independently from known distributions, and presented in a uniformly random order. A decision-maker must accept or reject each value when it is presented, and may accept at most $k$…
One of the classic problems in online decision-making is the *secretary problem* where to goal is to maximize the probability of choosing the largest number from a randomly ordered sequence. A natural extension allows selecting multiple…
We consider the classical problem of discrete distribution estimation using i.i.d. samples in a novel scenario where additional side information is available on the distribution. In large alphabet datasets such as text corpora, such side…
We consider online resource allocation problems where given a set of requests our goal is to select a subset that maximizes a value minus cost type of objective function. Requests are presented online in random order, and each request…
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 classical secretary problem has been generalized over the years into several directions. In this paper we confine our interest to those generalizations which have to do with the more general problem of stopping on a last observation of…
In the matroid secretary problem, the elements of a matroid $\mathcal{M}$ arrive in random order. Once we observe an item we need to irrevocably decide whether or not to accept it. The set of selected elements should form an independent set…
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…