Related papers: Prophet Secretary Through Blind Strategies
We present a general framework for stochastic online maximization problems with combinatorial feasibility constraints. The framework establishes prophet inequalities by constructing price-based online approximation algorithms, a natural…
We revisit three fundamental problems in algorithms under uncertainty: the Secretary Problem, Prophet Inequality, and Stochastic Probing, each subject to general downward-closed constraints. When elements have binary values, all three…
We study the prophet inequality when the gambler has an access only to a single sample from each distribution. Rubinstein, Wang and Weinberg showed that an optimal guarantee of 1/2 can be achieved when the underlying matroid has rank 1,…
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 study a pricing problem where a seller has $k$ identical copies of a product, buyers arrive sequentially, and the seller prices the items aiming to maximize social welfare. When $k=1$, this is the so called "prophet inequality" problem…
Prophet inequalities are fundamental optimal stopping problems, where a decision-maker observes sequentially items with values sampled independently from known distributions, and must decide at each new observation to either stop and gain…
Prophet inequalities are performance guarantees for online algorithms (a.k.a. stopping rules) solving the following "hiring problem": a decision maker sequentially inspects candidates whose values are independent random numbers and is asked…
In learning-augmented online algorithms, predictions are usually valued for what they say: a value estimate, a solution, or an algorithmic recommendation. This paper shows that predictions can also be valuable solely due to their arrival…
We study the classic single-choice prophet inequality problem through a resource augmentation lens. Our goal is to bound the $(1-\varepsilon)$-competition complexity of different types of online algorithms. This metric asks for the smallest…
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 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…
The value maximization version of the secretary problem is the problem of hiring a candidate with the largest value from a randomly ordered sequence of candidates. In this work, we consider a setting where predictions of candidate values…
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…
For many online problems, it is known that the uniform arrival order enables the design of algorithms with much better performance guarantees than under worst-case. The quintessential example is the secretary problem. If the sequence of…
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…
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…
The prophet inequality is one of the cornerstone problems in optimal stopping theory and has become a crucial tool for designing sequential algorithms in Bayesian settings. In the i.i.d. $k$-selection prophet inequality problem, we…
We study the polynomial-time approximability of the optimal online stochastic bipartite matching algorithm, initiated by Papadimitriou et al. (EC'21). Here, nodes on one side of the graph are given upfront, while at each time $t$, an online…
We study matroid prophet inequalities when distributions are unknown and accessible only through samples. While single-sample prophet inequalities for special matroids are known, no constant-factor competitive algorithm with even a…
We solve the secretary problem in the case that the ranked items arrive in a statistically biased order rather than in uniformly random order. The bias is given by a Mallows distribution with parameter $q\in(0,1)$, so that higher ranked…