2019/09/01 by Shaojie Tang, Tang, Shaojie
Computer Science · Mathematics · #Algorithm #Budget constraint #Complexity and Algorithms in Graphs #Computer science #Constraint (computer-aided design) #Cryptography and Data Security #Data Structures and Algorithms (cs.DS) #Economics #FOS: Computer and information sciences #FOS: Mathematics #Machine Learning (cs.LG) #Mathematical economics #Mathematical optimization #Mathematics #Maximization #Microeconomics #Optimization and Control (math.OC) #Optimization and Search Problems #Set (abstract data type) #State (computer science) #Submodular set function #cs.DS #cs.LG #math.OC
paper · pdf · doi:10.48550/arxiv.1909.01795
published in arXiv (Cornell University) (Cornell University) · This paper is accepted at The 15th International Conference on Algorithmic Aspects in Information and Management (AAIM 2021)
openalex publication_date 2019/09/01 · arxiv created 2021/11/11 · arxiv updated 2021/11/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06
In this paper, we study a new stochastic submodular maximization problem with state-dependent costs and rejections. The input of our problem is a budget constraint B, and a set of items whose states (i.e., the marginal contribution and the cost of an item) are drawn from a known probability distribution. The only way to know the realized state of an item is to probe that item. We allow rejections, i.e., after probing an item and knowing its actual state, we must decide immediately and irrevocably whether to add that item to our solution or not. Our objective is to sequentially probe/selet a best group of items subject to a budget constraint on the total cost of the selected items. We present a constant approximate solution to this problem. We show that our solution can be extended to an online setting.