Related papers: Prophet Secretary: Surpassing the $1-1/e$ Barrier
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…
The secretary problem or the game of Googol are classic models for online selection problems that have received significant attention in the last five decades. We consider a variant of the problem and explore its connections to data-driven…
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…
In this paper, we introduce an over-time variant of the well-known prophet inequality with i.i.d. random variables. Instead of stopping with one realized value at some point in the process, we decide for each step how long we select 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…
In a classical online decision problem, a decision-maker who is trying to maximize her value inspects a sequence of arriving items to learn their values (drawn from known distributions), and decides when to stop the process by taking the…
In the prophet inequality problem, a gambler faces a sequence of items arriving online with values drawn independently from known distributions. On seeing an item, the gambler must choose whether to accept its value as her reward and quit…
A prophet inequality states, for some $\alpha\in[0,1]$, that the expected value achievable by a gambler who sequentially observes random variables $X_1,\dots,X_n$ and selects one of them is at least an $\alpha$ fraction of the maximum value…
Prophet inequalities compare online stopping strategies against an omniscient "prophet" using distributional knowledge. In this work, we augment this model with a conservative prediction of the maximum realized value. We quantify the…
The prophet and secretary problems demonstrate online scenarios involving the optimal stopping theory. In a typical prophet or secretary problem, selection decisions are assumed to be immediate and irrevocable. However, many online settings…
For many online problems, it is known that the uniform arrival order enables the design of algorithms with much better performance guarantees than under worst-case. The quintessential example is the secretary problem. If the sequence of…
A central object in optimal stopping theory is the single-choice prophet inequality for independent, identically distributed random variables: Given a sequence of random variables $X_1,\dots,X_n$ drawn independently from a distribution $F$,…
We introduce the \textit{prophet inequality with uncertain acceptance} model, in which a decision maker sequentially observes a sequence of independent options, each characterized by a value $x_i$ and an acceptance probability $p_i$, both…
We study the single-choice Prophet Inequality problem when the gambler is given access to samples. We show that the optimal competitive ratio of $1/2$ can be achieved with a single sample from each distribution. When the distributions are…
The rich literature on online Bayesian selection problems has long focused on so-called prophet inequalities, which compare the gain of an online algorithm to that of a "prophet" who knows the future. An equally-natural, though…
We study the classic single-choice prophet secretary problem through a resource augmentation lens. Our goal is to bound the $(1-\epsilon)$-competition complexity for different classes of online algorithms. This metric asks for the smallest…
We study the prophet inequality, a fundamental problem in online decision-making and optimal stopping, in a practical setting where rewards are observed only through noisy realizations and reward distributions are unknown. At each stage,…
In the classical prophet inequality, a gambler faces a sequence of items, whose values are drawn independently from known distributions. Upon the arrival of each item, its value is realized and the gambler either accepts it and the game…
Prophet inequalities are a cornerstone in optimal stopping and online decision-making. Traditionally, they involve the sequential observation of $n$ non-negative independent random variables and face irrevocable accept-or-reject choices.…
Prophet inequality concerns a basic optimal stopping problem and states that simple threshold stopping policies -- i.e., accepting the first reward larger than a certain threshold -- can achieve tight $\frac{1}{2}$-approximation to the…