CAREER: Large Scale Stochastic Optimization and Statistics

职业：大规模随机优化和统计

• 批准号: 1541099
• 负责人: Philippe Rigollet
• 金额: $ 20.87万
• 依托单位: Massachusetts Institute of Technology
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2015
• 资助国家: 美国
• 起止时间: 2015-02-01 至 2017-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1541099&HistoricalAwards=false
• 关键词: CAREER; Large; Scale; Stochastic; Optimization

Stochastic optimization offers a general framework to study many fundamental statistical problems related to prediction such as regression, classification and density estimation. Furthermore, it is a natural framework to import powerful algorithms from numerical optimization, especially for large scale problems. The broad goal of this project is to understand the fundamental interactions between statistics and stochastic optimization. To accomplish this task the investigator (a) identifies new problems from statistics, especially with complex structure, that can be recast as stochastic optimization problems; (b) develops new algorithms that optimally and efficiently solve large scale problems; (c) determines essential characteristics of the problems that govern the performance of algorithms and their fundamental limitations; and (d) explores peripheral problems of stochastic optimization including stochastic optimization with stochastic constraints and stochastic optimization with limited feedback. The information era has witnessed an explosion in the collection of data and large scale data sets are ubiquitous in a wide range of applications including biology, networks, environmental science, sociology and marketing. This results in an acute need of new statistical methods to analyze these data sets of unprecedented size. While techniques from numerical optimization can be used in several scenarios, their analysis remains largely dissociated from that of the statistical task at hand. This research aims at providing a unified treatment of a number of large scale problems emerging from statistical learning and from optimization under uncertainty in general. Therefore, the project will not only result in new and effective algorithms, but also in a novel theoretical framework that supports the analysis of stochastic optimization problems and enables further improvements of said algorithms.

随机优化提供了一个一般框架，可以研究与预测有关的许多基本统计问题，例如回归，分类和密度估计。此外，它是从数值优化中导入强大算法的自然框架，尤其是对于大规模问题。该项目的广泛目标是了解统计和随机优化之间的基本相互作用。为了完成这项任务，研究人员（a）确定了统计数据中的新问题，尤其是在复杂的结构中，可以将其重塑为随机优化问题； （b）开发了最佳有效地解决大规模问题的新算法； （c）确定控制算法性能及其基本局限性的问题的基本特征； （d）探讨随机优化的外围问题，包括随机约束和随机优化的随机优化，反馈有限。信息时代目睹了数据收集的爆炸，大规模数据集在包括生物学，网络，环境科学，社会学和营销在内的广泛应用中无处不在。这导致急需新的统计方法来分析这些空前大小的数据集。虽然可以在几种情况下使用来自数值优化的技术，但它们的分析仍与当前统计任务的分析基本分离。这项研究旨在提供统一的处理，从统计学习和一般不确定性下的优化出现的许多大规模问题。因此，该项目不仅会导致新的和有效的算法，而且还将在一个支持随机优化问题分析的新型理论框架中，并能够进一步改进上述算法。