Discrete Optimization Algorithm for Machine Learning via Discrete Convex Analysis

2018 Fiscal Year Final Research Report

• Project/Area Number: 16K16011
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Multi-year Fund
• Research Field: Mathematical informatics
• Research Institution: Institute of Physical and Chemical Research (2017-2018); Shizuoka University (2016)
• Principal Investigator: Maehara Takanori 国立研究開発法人理化学研究所, 革新知能統合研究センター, ユニットリーダー (20751407)
• Project Period (FY): 2016-04-01 – 2019-03-31
• Keywords: 組合せ最適化 / 離散凸解析 / 機械学習

Outline of Final Research Achievements

Combinatorial optimization problems are required to solve in machine learning applications for, e.g., optimal decision making and feature selection. Submodular functions are a typical class of objective functions appeared in this context. Submodular functions satisfy the diminishing return property, which is a natural property of human utility and information, and are regarded as a discrete analogue of continuous convex functions. Discrete convex analysis is a theoretical framework to analyze the property of submodular functions (and its related class of functions) via the analogy of of convex functions. In this study, we establish a combinatorial optimization algorithm that can be applied to machine-learning problems using the discrete convex analysis.

Free Research Field

組合せ最適化; 機械学習

Academic Significance and Societal Importance of the Research Achievements

機械学習は近年極めて注目を集めている分野である．深層学習等の予測問題は適当な確率モデルのパラメタ最適化（連続最適化）問題として定式化され，大規模な計算能力の支援のもと確率勾配法などの汎用手法で解かれている．一方で，得られた予測結果から具体的な戦略を定める戦略決定問題や，モデルを圧縮する部分集合選択などは離散最適化問題となるが，これらに対する汎用的な解法は現在のところ存在しない．本研究ではそのような手法の理論基盤を作ることを目的とし，離散凸解析に基づくアルゴリズムを提案した．