Related papers: Prophet Inequalities with Cancellation Costs
In the prophet inequality problem, a gambler faces a sequence of items arriving online with values drawn independently from known distributions. On seeing an item, the gambler must choose whether to accept its value as her reward and quit…
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 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…
Prophet inequalities bound the expected reward that can be obtained in a stopping problem by the optimal reward of its corresponding off-line version. We propose a systematic technique for deriving prophet inequalities for stopping problems…
A prophet inequality states, for some $\alpha\in[0,1]$, that the expected value achievable by a gambler who sequentially observes random variables $X_1,\dots,X_n$ and selects one of them is at least an $\alpha$ fraction of the maximum value…
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 initiate the study of two-sided online resource allocation with costly cancellations. Our focus is on edge-weighted online bipartite matching (and several of its extensions), where nodes arrive online and request offline resources. In…
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…
In the adaptive ProbeMax problem, given a collection of mutually-independent random variables $X_1, \ldots, X_n$, our goal is to design an adaptive probing policy for sequentially sampling at most $k$ of these variables, with the objective…
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 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 devise a general graph-theoretic framework for studying prophet inequalities. In this framework, an agent traverses a directed acyclic graph from a starting node $s$ to a target node $t$. Each edge has a value that is sampled from a…
We present pricing mechanisms for several online resource allocation problems which obtain tight or nearly tight approximations to social welfare. In our settings, buyers arrive online and purchase bundles of items; buyers' values for the…
The setting of the classic prophet inequality is as follows: a gambler is shown the probability distributions of $n$ independent, non-negative random variables with finite expectations. In their indexed order, a value is drawn from each…
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 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 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…
We consider a combinatorial auction setting where buyers have fractionally subadditive (XOS) valuations over the items and the seller's objective is to maximize the social welfare. A prophet inequality in this setting bounds the competitive…
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 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…