Related papers: Prophet Inequality with Conservative Prediction
In this paper, we introduce an over-time variant of the well-known prophet inequality with i.i.d. random variables. Instead of stopping with one realized value at some point in the process, we decide for each step how long we select the…
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…
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…
We study the prophet inequality, a fundamental problem in online decision-making and optimal stopping, in a practical setting where rewards are observed only through noisy realizations and reward distributions are unknown. At each stage,…
The classical Prophet Inequality arises from a fundamental problem in optimal-stopping theory. In this problem, a gambler sees a finite sequence of independent, non-negative random variables. If he stops the sequence at any time, he…
In this work, we study the single-choice prophet inequality problem, where a gambler faces a sequence of~$n$ online i.i.d. random variables drawn from an unknown distribution. When a variable reveals its value, the gambler needs to decide…
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…
Optimal stopping theory is a powerful tool for analyzing scenarios such as online auctions in which we generally require optimizing an objective function over the space of stopping rules for an allocation process under uncertainty. Perhaps…
We explore a prophet inequality problem, where the values of a sequence of items are drawn i.i.d. from some distribution, and an online decision maker must select one item irrevocably. We establish that $\mathrm{CR}_{\ell}$ the worst-case…
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…
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…
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 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…
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…
In the prophet inequality problem, a gambler faces a sequence of items arriving online with values drawn independently from known distributions. On seeing an item, the gambler must choose whether to accept its value as her reward and quit…
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…
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 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…
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 a classical online decision problem, a decision-maker who is trying to maximize her value inspects a sequence of arriving items to learn their values (drawn from known distributions), and decides when to stop the process by taking the…