Exploration of integrated approach to data-driven optimization models

2018 Fiscal Year Final Research Report

• Project/Area Number: 15K01204
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Social systems engineering/Safety system
• Research Institution: Chuo University
• Principal Investigator: Gotoh Jun-ya 中央大学, 理工学部, 教授 (40334031)
• Research Collaborator: TAKEDA Akiko ; TAKANO Yuichi ; TONO Katsuya ; URYASEV Stan ; LIM Andrew E. B. ; KIM Michael J.
• Project Period (FY): 2015-04-01 – 2019-03-31
• Keywords: 数理最適化 / データ解析 / ロバスト最適化 / 機械学習

Outline of Final Research Achievements

By combining optimization methods for decision making under uncertainty such as stochastic programming and robust optimization with methodologies developed in various fields and contexts such as risk management, machine learning, and signal processing, we provide general-purposed methods. Two outcomes form the major part of obtained results. For the first thing, based on the observation that a class of distributed robust optimization models can be approximated by the so-called mean-variance optimization model when a hyper-parameter is sufficiently small, we got suggestions for how to tune the parameter. The second is a method for presenting the so-called cardinality constraint that appears in contexts such as variable selection of statistical models by using a continuous optimization formulation. We also studied local search algorithms for those problems.

Free Research Field

数理最適化、オペレーションズリサーチ

Academic Significance and Societal Importance of the Research Achievements

不確実性を考慮した意思決定の重要性は容易に認識されるが、その方法論は様々な形をとる。本研究課題の成果は最適化モデリングという、1つのレンズを通して、一見異なるものを眺めることで、既に多くの研究者コミュニティにおいてあまり疑問を持たれずに利用されている方法に対し、中立的立場から検討を行い、汎用性のある手法を提示したものと考える。これにより、既存の方法論の限界や欠点、特徴が理解しやすくなると同時に、新たな方法論の創出にも寄与する可能性があると考える。