Related papers: Prophet Inequalities Require Only a Constant Numbe…
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…
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,…
We consider the prophet inequality problem for (not necessarily bipartite) matching problems with independent edge values, under both edge arrivals and vertex arrivals. We show constant-factor prophet inequalities for the case where the…
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…
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…
In the classical optimal stopping problem, a player is given a sequence of random variables $X_1\ldots X_n$ with known distributions. After observing the realization of $X_i$, the player can either accept the observed reward from $X_i$ and…
In our problem, we are given access to a number of sequences of nonnegative i.i.d. random variables, whose realizations are observed sequentially. All sequences are of the same finite length. The goal is to pick one element from each…
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…
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…
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,…
We introduce a model of competing agents in a prophet setting, where rewards arrive online, and decisions are made immediately and irrevocably. The rewards are unknown from the outset, but they are drawn from a known probability…
We study the prophet inequality when the gambler has an access only to a single sample from each distribution. Rubinstein, Wang and Weinberg showed that an optimal guarantee of 1/2 can be achieved when the underlying matroid has rank 1,…
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…
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…
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…
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 a pricing problem where a seller has $k$ identical copies of a product, buyers arrive sequentially, and the seller prices the items aiming to maximize social welfare. When $k=1$, this is the so called "prophet inequality" problem…
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…
The prophet inequalities problem has received significant study over the past decades and has several applications such as to online auctions. In this paper, we study two variants of the i.i.d. prophet inequalities problem, namely 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.…