Related papers: Pandora's Box Problem with Order Constraints
The Gittins index is a tool that optimally solves a variety of decision-making problems involving uncertainty, including multi-armed bandit problems, minimizing mean latency in queues, and search problems like the Pandora's box model.…
We study the problem of sorting under incomplete information, when queries are used to resolve uncertainties. Each of $n$ data items has an unknown value, which is known to lie in a given interval. We can pay a query cost to learn the…
The Correlated Pandora's Problem posed by Chawla et al. (2020) generalizes the classical Pandora's Problem by allowing the numbers inside the Pandora's boxes to be correlated. It also generalizes the Min Sum Set Cover problem, and is…
Consider a network design application where we wish to lay down a minimum-cost spanning tree in a given graph; however, we only have stochastic information about the edge costs. To learn the precise cost of any edge, we have to conduct a…
We investigate the role of commitment in optimal stopping by studying all the variants between Prophet Inequality (PI) and Pandora's Box (PB). Both problems deal with a set of variables drawn from known distributions. In PI the gambler…
We study a sequential resource allocation problem motivated by adaptive network recruitment, in which a limited budget of identical resources must be allocated over multiple rounds to individuals with stochastic referral capacity.…
We consider the problem of designing an adaptive sequence of questions that optimally classify a candidate's ability into one of several categories or discriminative grades. A candidate's ability is modeled as an unknown parameter, which,…
The main contribution of this paper resides in providing novel algorithmic advances and analytical insights for the sequential hiring problem, a recently introduced dynamic optimization model where a firm adaptively fills a limited number…
In this paper we study a single machine scheduling problem with the objective of minimizing the sum of completion times. Each of the given jobs is either short or long. However the processing times are initially hidden to the algorithm, but…
The optimization of expensive-to-evaluate black-box functions over combinatorial structures is an ubiquitous task in machine learning, engineering and the natural sciences. The combinatorial explosion of the search space and costly…
In digital health and EdTech, recommendation systems face a significant challenge: users often choose impulsively, in ways that conflict with the platform's long-term payoffs. This misalignment makes it difficult to effectively learn to…
We consider various stochastic models that incorporate the notion of risk-averseness into the standard 2-stage recourse model, and develop novel techniques for solving the algorithmic problems arising in these models. A key notable feature…
Solving optimal stopping problems by backward induction in high dimensions is often very complex since the computation of conditional expectations is required. Typically, such computations are based on regression, a method that suffers from…
We study a fundamental stochastic selection problem involving $n$ independent random variables, each of which can be queried at some cost. Given a tolerance level $\delta$, the goal is to find a value that is $\delta$-approximately minimum…
Packing problems are an important class of optimization problems. The probably most well-known problem if this type is knapsack and many generalizations of it have been studied in the literature like Two-dimensional Geometric Knapsack…
In the restricted assignment problem, the input consists of a set of machines and a set of jobs each with a processing time and a subset of eligible machines. The goal is to find an assignment of the jobs to the machines minimizing the…
We develop an approach for solving rooted orienteering problems with category constraints as found in tourist trip planning and logistics. It is based on expanding partial solutions in a systematic way, prioritizing promising ones, which…
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…
A simple problem is studied in which there are N boxes and a prize known to be in one of the boxes. Furthermore, the probability that the prize is in any box is given. It is desired to find the prize with minimal expected work, where it…
We consider a simple optimal probabilistic problem solving strategy that searches through potential solution candidates in a specific order. We are interested in what impact has interchanging the order of two solution candidates with…