Related papers: Predict and Match: Prophet Inequalities with Uncer…
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 consider a practically motivated variant of the canonical online fair allocation problem: a decision-maker has a budget of perishable resources to allocate over a fixed number of rounds. Each round sees a random number of arrivals, and…
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…
We study fair division of indivisible goods in a single-parameter environment. In particular, we develop truthful social welfare maximizing mechanisms for fairly allocating indivisible goods. Our fairness guarantees are in terms of solution…
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…
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 consider online learning when the time horizon is unknown. We apply a minimax analysis, beginning with the fixed horizon case, and then moving on to two unknown-horizon settings, one that assumes the horizon is chosen randomly according…
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…
Prophet inequalities compare the expected performance of an online algorithm for a stochastic optimization problem to the expected optimal solution in hindsight. They are a major alternative to classic worst-case competitive analysis, of…
We study the online fair division problem, where indivisible goods arrive sequentially and must be allocated immediately and irrevocably. Prior work establishes strong impossibility results for approximating classic notions such as…
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 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…
The prophet secretary problem is a combination of the prophet inequality and the secretary problem, where elements are drawn from known independent distributions and arrive in uniformly random order. In this work, we design 1) a…
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…
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…
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 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 $F$,…
As we all know, users and item-providers are two main parties of participants in recommender systems. However, most existing research efforts on recommendation were focused on better serving users and overlooked the purpose of…
In this paper, we study $k$-unit single sample prophet inequalities. A seller has $k$ identical, indivisible items to sell. A sequence of buyers arrive one-by-one, with each buyer's private value for the item, $X_i$, revealed to the seller…