Related papers: Optimal Stopping with a Predicted Prior
Optimal stopping theory is a powerful tool for analyzing scenarios such as online auctions in which we generally require optimizing an objective function over the space of stopping rules for an allocation process under uncertainty. Perhaps…
We take a unifying approach to single selection optimal stopping problems with random arrival order and independent sampling of items. In the problem we consider, a decision maker (DM) initially gets to sample each of $N$ items…
Many online problems are studied in stochastic settings for which inputs are samples from a known distribution, given in advance, or from an unknown distribution. Such distributions model both beyond-worst-case inputs and, when given,…
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…
We study online selection problems in both the prophet and secretary settings, when arriving agents have interdependent values. In the interdependent values model, introduced in the seminal work of Milgrom and Weber [1982], each agent has a…
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…
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…
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…
In a prophet inequality problem, $n$ independent random variables are presented to a gambler one by one. The gambler decides when to stop the sequence and obtains the most recent value as reward. We evaluate a stopping rule by the…
In the classic prophet inequality, samples from independent random variables arrive online. A gambler that knows the distributions must decide at each point in time whether to stop and pick the current sample or to continue and lose that…
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 $F$,…
The classical Prophet Inequality arises from a fundamental problem in optimal-stopping theory. In this problem, a gambler sees a finite sequence of independent, non-negative random variables. If he stops the sequence at any time, he…
We study the prophet secretary problem, a well-studied variant of the classic prophet inequality, where values are drawn from independent known distributions but arrive in uniformly random order. Upon seeing a value at each step, the…
Prophet inequalities for rewards maximization are fundamental to optimal stopping theory with extensive applications to mechanism design and online optimization. We study the \emph{cost minimization} counterpart of the classical prophet…
This paper considers a finite horizon optimal stopping problem for a sequence of independent and identically distributed random variables, where the objective is to design stopping rules that attempt to select the random variable with the…
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…
Prophet inequalities are a central object of study in optimal stopping theory. A gambler is sent values in an online fashion, sampled from an instance of independent distributions, in an adversarial, random or selected order, depending on…
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…
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 the repeated optimal stopping problem, in which the same optimal stopping instance with an unknown distribution is solved repeatedly over $T$ rounds. We aim to simultaneously achieve strong per-round performance guarantees relative…