Related papers: Prophet Inequalities via the Expected Competitive …
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…
In a prophet inequality problem, $n$ independent random variables are presented to a gambler one by one. The gambler decides when to stop the sequence and obtains the most recent value as reward. We evaluate a stopping rule by the…
We study a variant of the single-choice prophet inequality problem where the decision-maker does not know the underlying distribution and has only access to a set of samples from the distributions. Rubinstein et al. [2020] showed that the…
We introduce a model of competing agents in a prophet setting, where rewards arrive online, and decisions are made immediately and irrevocably. The rewards are unknown from the outset, but they are drawn from a known probability…
In the classical prophet inequality, a gambler faces a sequence of items, whose values are drawn independently from known distributions. Upon the arrival of each item, its value is realized and the gambler either accepts it and the game…
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…
In the classical prophet inequality settings, a gambler is given a sequence of $n$ random variables $X_1, \dots, X_n$, taken from known distributions, observes their values in this (potentially adversarial) order, and select one of them,…
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…
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…
In this work we initiate the study of buy-and-sell prophet inequalities. We start by considering what is arguably the most fundamental setting. In this setting the online algorithm observes a sequence of prices one after the other. At each…
Free order prophet inequalities bound the ratio between the expected value obtained by two parties each selecting a value from a set of independent random variables: a "prophet" who knows the value of each variable and may select the…
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…
Prophet inequality concerns a basic optimal stopping problem and states that simple threshold stopping policies -- i.e., accepting the first reward larger than a certain threshold -- can achieve tight $\frac{1}{2}$-approximation to the…
A prophet inequality states, for some $\alpha\in[0,1]$, that the expected value achievable by a gambler who sequentially observes random variables $X_1,\dots,X_n$ and selects one of them is at least an $\alpha$ fraction of the maximum value…
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…
Most of the literature on online algorithms in revenue management focuses on settings with irrevocable decisions, where once a decision is made upon the arrival of a new input, it cannot be canceled later. Motivated by modern applications…
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 $F$,…
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…
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 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…