Related papers: The Competition Complexity of Prophet Inequalities
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…
Competition complexity formalizes a compelling intuition: rather than refining the mechanism, how much additional competition is sufficient for a simple mechanism to compete with an optimal one? We begin the study of this question in…
We initiate the study of the prophet inequality problem through the resource augmentation framework in scenarios when the values of the rewards are correlated. Our goal is to determine the number of additional rewards an online algorithm…
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…
In this work, we study the single-choice prophet inequality problem, where a gambler faces a sequence of~$n$ online i.i.d. random variables drawn from an unknown distribution. When a variable reveals its value, the gambler needs to decide…
In this work we initiate the study of buy-and-sell prophet inequalities. We start by considering what is arguably the most fundamental setting. In this setting the online algorithm observes a sequence of prices one after the other. At each…
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 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…
We explore a prophet inequality problem, where the values of a sequence of items are drawn i.i.d. from some distribution, and an online decision maker must select one item irrevocably. We establish that $\mathrm{CR}_{\ell}$ the worst-case…
We present a general framework for stochastic online maximization problems with combinatorial feasibility constraints. The framework establishes prophet inequalities by constructing price-based online approximation algorithms, a natural…
Prophet inequalities consist of many beautiful statements that establish tight performance ratios between online and offline allocation algorithms. Typically, tightness is established by constructing an algorithmic guarantee and a…
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 a variant of the single-choice prophet inequality problem where the decision-maker does not know the underlying distribution and has only access to a set of samples from the distributions. Rubinstein et al. [2020] showed that 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,…
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…
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 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…
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 I.I.D. Prophet Inequality is a fundamental problem where, given $n$ independent random variables $X_1,\dots,X_n$ drawn from a known distribution $\mathcal{D}$, one has to decide at every step $i$ whether to stop and accept $X_i$ or…
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…