Related papers: Prophet Inequality: Order selection beats random o…
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…
Prophet inequalities are a central object of study in optimal stopping theory. In the iid model, a gambler sees values in an online fashion, sampled independently from a given distribution. Upon observing each value, the gambler either…
Consider a gambler and a prophet who observe a sequence of independent, non-negative numbers. The gambler sees the numbers one-by-one whereas the prophet sees the entire sequence at once. The goal of both is to decide on fractions of each…
We consider prophet inequalities under downward-closed constraints. In this problem, a decision-maker makes immediate and irrevocable choices on arriving elements, subject to constraints. Traditionally, performance is compared to the…
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…
There is a rising interest for studying the online benchmark as an alternative of the classical offline benchmark in online stochastic settings. Ezra, Feldman, Gravin, and Tang (SODA 2023) introduced the notion of order-competitive ratio,…
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…
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 Prophet Secretary problem, samples from a known set of probability distributions arrive one by one in a uniformly random order, and an algorithm must irrevocably pick one of the samples as soon as it arrives. The goal is to maximize…
We introduce a variant of the classic prophet inequality, called \emph{residual prophet inequality} (RPI). In the RPI problem, we consider a finite sequence of $n$ nonnegative independent random values with known distributions, and a known…
We study the classic single-choice prophet inequality problem through a resource augmentation lens. Our goal is to bound the $(1-\varepsilon)$-competition complexity of different types of online algorithms. This metric asks for the smallest…
The prophet secretary problem is a combination of the prophet inequality and the secretary problem, where elements are drawn from known independent distributions and arrive in uniformly random order. In this work, we design 1) a…
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 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 measure of order-competitive ratio introduced by Ezra et al. [2023] for online algorithms in Bayesian combinatorial settings. In our setting, a decision-maker observes a sequence of elements that are associated with stochastic…
Prophet inequalities compare the expected performance of an online algorithm for a stochastic optimization problem to the expected optimal solution in hindsight. They are a major alternative to classic worst-case competitive analysis, of…
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…
We study a continuous and infinite time horizon counterpart to the classic prophet inequality, which we term the stationary prophet inequality problem. Here, copies of a good arrive and perish according to Poisson point processes. Buyers…
We introduce a new measure for the performance of online algorithms in Bayesian settings, where the input is drawn from a known prior, but the realizations are revealed one-by-one in an online fashion. Our new measure is called…
Prophet inequalities are performance guarantees for online algorithms (a.k.a. stopping rules) solving the following "hiring problem": a decision maker sequentially inspects candidates whose values are independent random numbers and is asked…