{"title":"具有最优性保证的 A 优化实验设计一阶贪婪算法","authors":"Christian Aarset","doi":"arxiv-2409.09963","DOIUrl":null,"url":null,"abstract":"Optimal experimental design (OED) concerns itself with identifying ideal\nmethods of data collection, e.g.~via sensor placement. The \\emph{greedy\nalgorithm}, that is, placing one sensor at a time, in an iteratively optimal\nmanner, stands as an extremely robust and easily executed algorithm for this\npurpose. However, it is a priori unclear whether this algorithm leads to\nsub-optimal regimes. Taking advantage of the author's recent work on non-smooth\nconvex optimality criteria for OED, we here present a framework for verifying\nglobal optimality for the greedy algorithm, as well as employing gradient-based\nspeed-ups.","PeriodicalId":501286,"journal":{"name":"arXiv - MATH - Optimization and Control","volume":"44 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"A first-order greedy algorithm for A-optimal experimental design with optimality guarantee\",\"authors\":\"Christian Aarset\",\"doi\":\"arxiv-2409.09963\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Optimal experimental design (OED) concerns itself with identifying ideal\\nmethods of data collection, e.g.~via sensor placement. The \\\\emph{greedy\\nalgorithm}, that is, placing one sensor at a time, in an iteratively optimal\\nmanner, stands as an extremely robust and easily executed algorithm for this\\npurpose. However, it is a priori unclear whether this algorithm leads to\\nsub-optimal regimes. Taking advantage of the author's recent work on non-smooth\\nconvex optimality criteria for OED, we here present a framework for verifying\\nglobal optimality for the greedy algorithm, as well as employing gradient-based\\nspeed-ups.\",\"PeriodicalId\":501286,\"journal\":{\"name\":\"arXiv - MATH - Optimization and Control\",\"volume\":\"44 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-09-16\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"arXiv - MATH - Optimization and Control\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/arxiv-2409.09963\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - MATH - Optimization and Control","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2409.09963","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
摘要
优化实验设计(OED)关注的是确定理想的数据收集方法,例如通过传感器的放置。emph{greedyalgorithm},即以迭代优化的方式一次放置一个传感器,是一种极其稳健且易于执行的算法。然而,这种算法是否会导致次优状态,目前尚不清楚。利用作者最近在 OED 非光滑凸优化标准方面的研究成果,我们在此提出一个框架,用于验证贪婪算法的全局最优性,并采用基于梯度的加速方法。
A first-order greedy algorithm for A-optimal experimental design with optimality guarantee
Optimal experimental design (OED) concerns itself with identifying ideal
methods of data collection, e.g.~via sensor placement. The \emph{greedy
algorithm}, that is, placing one sensor at a time, in an iteratively optimal
manner, stands as an extremely robust and easily executed algorithm for this
purpose. However, it is a priori unclear whether this algorithm leads to
sub-optimal regimes. Taking advantage of the author's recent work on non-smooth
convex optimality criteria for OED, we here present a framework for verifying
global optimality for the greedy algorithm, as well as employing gradient-based
speed-ups.