Related papers: Prophets Inequalities with Uncertain Acceptance
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 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…
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…
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 problem of selling perishable items to a stream of buyers in order to maximize social welfare. A seller starts with a set of identical items, and each arriving buyer wants any one item, and has a valuation drawn i.i.d. from…
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 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…
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…
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…
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…
There are two major models of value uncertainty in the optimal stopping literature: the secretary model, which assumes no prior knowledge, and the prophet inequality model, which assumes full information about value distributions. In…
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…
We study threshold testing, an elementary probing model with the goal to choose a large value out of $n$ i.i.d. random variables. An algorithm can test each variable $X_i$ once for some threshold $t_i$, and the test returns binary feedback…
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…
Due to numerous applications in retail and (online) advertising the problem of assortment selection has been widely studied under many combinations of discrete choice models and feasibility constraints. In many situations, however, an…
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 study the i.i.d. $k$-selection prophet inequality problem, where a decision-maker sequentially observes $n$ independent nonnegative rewards and may accept at most $k$ of them without knowledge of future realizations. The objective is to…
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…
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…
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…