Related papers: Non-Adaptive Matroid Prophet Inequalities
In the online 2-bounded auction problem, we have a collection of items represented as nodes in a graph and bundles of size two represented by edges. Agents are presented sequentially, each with a random weight function over the bundles. The…
Prophet inequalities and secretary problems have been extensively studied in recent years due to their elegance, connections to online algorithms, stochastic optimization, and mechanism design problems in game theoretic settings. Rubinstein…
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…
The secretary and the prophet inequality problems are central to the field of Stopping Theory. Recently, there has been a lot of work in generalizing these models to multiple items because of their applications in mechanism design. The most…
We consider prophet inequalities subject to feasibility constraints that are the intersection of $q$ matroids. The best-known algorithms achieve a $\Theta(q)$-approximation, even when restricted to instances that are the intersection of $q$…
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…
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…
In the classical prophet inequality, a gambler observes a sequence of stochastic rewards $V_1,...,V_n$ and must decide, for each reward $V_i$, whether to keep it and stop the game or to forfeit the reward forever and reveal the next value…
Due to their numerous applications, in particular in Mechanism Design, Prophet Inequalities have experienced a surge of interest. They describe competitive ratios for basic stopping time problems where random variables get revealed…
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…
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 introduce a novel framework of Prophet Inequalities for combinatorial valuation functions. For a (non-monotone) submodular objective function over an arbitrary matroid feasibility constraint, we give an $O(1)$-competitive algorithm. For…
In modern sample-driven Prophet Inequality, an adversary chooses a sequence of $n$ items with values $v_1, v_2, \ldots, v_n$ to be presented to a decision maker (DM). The process follows in two phases. In the first phase (sampling phase),…
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…
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…
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…
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…
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…