CAREER: New Algorithms for Submodular Optimization

子模块优化为广泛的应用提供了通用的解决方案，从监控供水网络到汇总大型文档语料库和语音识别。现有的大多数子模优化算法都不适用于现代数据集，因为它们是针对最坏情况设计的，而且运行时间过长，经验性能较差。该项目旨在开发具有改进的经验性能的可扩展算法方法，用于子模块优化，并将理论见解转化为应用。这项拟议的研究汇集了计算机科学、数学和优化的见解，并加强了这些领域之间的联系。该项目将培训下一批学生，并为他们提供在所有这些领域工作的技术工具。该项目集中在子模函数优化方面的三个相互关联的研究方向：(A)设计更快的算法来最小化具有可分解或和结构的子模函数。方法是建立在来自离散和连续优化的丰富工具集上。(B)具有改进的逼近保证和更快的运行时间的约束子模最大化问题的设计算法。重点是解决非单调目标的约束子模极大问题的可逼近性，以及设计中心约束族的更快算法。(C)设计算法和框架，用于分配或标记具有分模块费用的问题。其主要目标是获得更具表现力的算法框架和高效的算法。

Submodular optimization provides general solutions to a wide range of applications from monitoring water distribution networks to summarizing large corpora of documents and speech recognition. Most of the existing submodular optimization algorithms are not suitable for modern datasets, since they are designed for worst-case instances and they suffer from prohibitive running times and poor empirical performance. This project aims to develop scalable algorithmic approaches with improved empirical performance for submodular optimization and to transfer theoretical insights to applications. The proposed research brings together insights from computer science, mathematics and optimization, and strengthens connections among these fields. The project will involve training the next wave of students and equipping them with technical tools to work in all these fields.The project focuses on three inter-related research directions in submodular function optimization: (a) Design faster algorithms for minimizing submodular functions with a decomposable or sum structure. The approach is to build on a rich set of tools from both discrete and continuous optimization. (b) Design algorithms for constrained submodular maximization problems with improved approximation guarantees and faster running times. The focus is on settling the approximability of constrained submodular maximization problems with a non-monotone objective and on designing faster algorithms for central families of constraints. (c) Design algorithms and frameworks for allocation or labeling problems with submodular costs. The main goal is to obtain more expressive algorithmic frameworks and efficient algorithms.