Related papers: Prophet Secretary: Surpassing the $1-1/e$ Barrier
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 introduce a new decomposition technique for random variables that maps a generic instance of the prophet inequalities problem to a new instance where all but a constant number of variables have a tractable structure that we refer to as…
We study various generalizations of the secretary problem with submodular objective functions. Generally, a set of requests is revealed step-by-step to an algorithm in random order. For each request, one option has to be selected so as to…
We present a number of positive and negative results for variants of the matroid secretary problem. Most notably, we design a constant-factor competitive algorithm for the "random assignment" model where the weights are assigned randomly to…
Online knapsack problem is considered, where items arrive in a sequential fashion that have two attributes; value and weight. Each arriving item has to be accepted or rejected on its arrival irrevocably. The objective is to maximize the sum…
Prophet inequalities and secretary problems have been extensively studied in recent years due to their elegance, connections to online algorithms, stochastic optimization, and mechanism design problems in game theoretic settings. Rubinstein…
In the secretary problem, a set of secretary candidates arrive in a uniformly random order and reveal their values one by one. A company, who can only hire one candidate and hopes to maximize the expected value of its hire, needs to make…
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…
Prophet inequalities bound the expected reward that can be obtained in a stopping problem by the optimal reward of its corresponding off-line version. We propose a systematic technique for deriving prophet inequalities for stopping problems…
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 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…
We study the problem of solving Packing Integer Programs (PIPs) in the online setting, where columns in $[0,1]^d$ of the constraint matrix are revealed sequentially, and the goal is to pick a subset of the columns that sum to at most $B$ in…
The elements of a finite nonempty partially ordered set are exposed at independent uniform times in $[0,1]$ to a selector who, at any given time, can see the structure of the induced partial order on the exposed elements. The selector's…
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…
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…
We present a new variant of the secretary problem. Let $A$ be a totally ordered set of $n$ \emph{applicants}. Given $P\subseteq A$ and $x\in A$, let $rr(P,x)=\vert\{z\in P \mid z\leq x\}\vert\mbox{ }$ be the \emph{relative rank of} $x$…
The prophet inequality is one of the cornerstone problems in optimal stopping theory and has become a crucial tool for designing sequential algorithms in Bayesian settings. In the i.i.d. $k$-selection prophet inequality problem, we…
We consider the online stochastic matching problem for bipartite graphs where edges adjacent to an online node must be probed to determine if they exist, based on known edge probabilities. Our algorithms respect commitment, in that if a…
In the classical prophet inequality settings, a gambler is given a sequence of $n$ random variables $X_1, \dots, X_n$, taken from known distributions, observes their values in this (potentially adversarial) order, and select one of them,…
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…