Related papers: Non-Adaptive Matroid Prophet Inequalities
We consider the problem of finding a basis of a matroid with weight exactly equal to a given target. Here weights can be discrete values from $\{-\Delta,\ldots,\Delta\}$ or more generally $m$-dimensional vectors of such discrete values. We…
Prophet inequalities are a central object of study in optimal stopping theory. A gambler is sent values in an online fashion, sampled from an instance of independent distributions, in an adversarial, random or selected order, depending on…
We introduce the \textit{prophet inequality with uncertain acceptance} model, in which a decision maker sequentially observes a sequence of independent options, each characterized by a value $x_i$ and an acceptance probability $p_i$, both…
We introduce NeuralProphet, a successor to Facebook Prophet, which set an industry standard for explainable, scalable, and user-friendly forecasting frameworks. With the proliferation of time series data, explainable forecasting remains a…
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 $F$,…
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…
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…
The study of the prophet inequality problem in the limited information regime was initiated by Azar et al. [SODA'14] in the pursuit of prior-independent posted-price mechanisms. As they show, $O(1)$-competitive policies are achievable using…
We introduce and study the weighted version of an online matching problem in the Euclidean plane with non-crossing constraints: points with non-negative weights arrive online, and an algorithm can match an arriving point to one of 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…
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…
We study generalizations of the "Prophet Inequality" and "Secretary Problem", where the algorithm is restricted to an arbitrary downward-closed set system. For {0,1}-values, we give O(log n)-competitive algorithms for both problems. This is…
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…
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…
Prophet inequalities are a useful tool for designing online allocation procedures and comparing their performance to the optimal offline allocation. In the basic setting of $k$-unit prophet inequalities, the well-known procedure of Alaei…
We consider prophet inequalities for XOS and MPH-$k$ combinatorial auctions and give a simplified proof for the existence of static and anonymous item prices which recover the state-of-the-art competitive ratios. Our proofs make use of a…
In the past decade, matrix factorization has been extensively researched and has become one of the most popular techniques for personalized recommendations. Nevertheless, the dot product adopted in matrix factorization based recommender…
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…
In the matroid buyback problem, an algorithm observes a sequence of bids and must decide whether to accept each bid at the moment it arrives, subject to a matroid constraint on the set of accepted bids. Decisions to reject bids are…
Suppose a customer is faced with a sequence of fluctuating prices, such as for airfare or a product sold by a large online retailer. Given distributional information about what price they might face each day, how should they choose when to…