Related papers: Prophet Inequalities via Linear Programming
A decisionmaker faces $n$ alternatives, each of which represents a potential reward. After investing costly resources into investigating the alternatives, the decisionmaker may select one, or more generally a feasible subset, and obtain the…
We study single-sample prophet inequalities (SSPIs), i.e., prophet inequalities where only a single sample from each prior distribution is available. Besides a direct, and optimal, SSPI for the basic single choice problem [Rubinstein et…
The prophet and secretary problems demonstrate online scenarios involving the optimal stopping theory. In a typical prophet or secretary problem, selection decisions are assumed to be immediate and irrevocable. However, many online settings…
We consider Bayesian online selection problem of a matching in bipartite graphs, i.e., online weighted matching problem with edge arrivals where online algorithm knows distributions of weights, that corresponds to the intersection of two…
This note records a common threshold/surplus decomposition for single-threshold stopping rules in the classical prophet inequality. The same decomposition is used to certify several deterministic thresholds, including the median, half-mean,…
We provide prophet inequality algorithms for online weighted matching in general (non-bipartite) graphs, under two well-studied arrival models, namely edge arrival and vertex arrival. The weight of each edge is drawn independently from an…
This work introduces \emph{sharding} and \emph{Poissonization} as a unified framework for analyzing prophet inequalities. Sharding involves splitting a random variable into several independent random variables, shards, that collectively…
Hill and Kertz studied the prophet inequality on iid distributions [The Annals of Probability 1982]. They proved a theoretical bound of $1-\frac{1}{e}$ on the approximation factor of their algorithm. They conjectured that the best…
We design novel mechanisms for welfare-maximization in two-sided markets. That is, there are buyers willing to purchase items and sellers holding items initially, both acting rationally and strategically in order to maximize utility. Our…
Consider a stream of $n$ random points (say, from the unit square) arriving one by one, where a player has to make an irreversible immediate decision for each arriving point whether to pick it. The player has to pick a single point, and the…
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 study a class of Bayesian online selection problems with matroid constraints. Consider a vendor who has several items to sell, with the set of sold items being subject to some structural constraints, e.g., the set of sold items should be…
The effectiveness of projection methods for solving systems of linear inequalities is investigated. It is shown that they have a computational advantage over some alternatives and that this makes them successful in real-world applications.…
The Prophet Inequality and Pandora's Box problems are fundamental stochastic problem with applications in Mechanism Design, Online Algorithms, Stochastic Optimization, Optimal Stopping, and Operations Research. A usual assumption in these…
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…
In the single stock trading prophet problem formulated by Correa et al.\ (2023), an online algorithm observes a sequence of prices of a stock. At each step, the algorithm can either buy the stock by paying the current price if it doesn't…
Despite having the same basic prophet inequality setup and model of loss aversion, conclusions in our multi-dimensional model differs considerably from the one-dimensional model of Kleinberg et al. For example, Kleinberg et al. gives a…
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…
Automating the solutions of multiple network information theory problems, stretching from fundamental concerns such as determining all information inequalities and the limitations of linear codes, to applied ones such as designing coded…
We study the repeated optimal stopping problem, in which the same optimal stopping instance with an unknown distribution is solved repeatedly over $T$ rounds. We aim to simultaneously achieve strong per-round performance guarantees relative…