Date of Award

8-1-2022

Language

English

Document Type

Dissertation

Degree Name

Doctor of Philosophy (PhD)

College/School/Department

Department of Mathematics and Statistics

Content Description

1 online resource (xi, 204 pages) : illustrations (some color)

Dissertation/Thesis Chair

Yiming YY Ying

Committee Members

Yunlong YF Feng, Penghang PY Yin

Keywords

Algorithmic Stability, Differential Privacy, Minimax Problems, Pairwise Learning, Stochastic Gradient Methods, Machine learning, Maxima and minima, Stochastic processes

Subject Categories

Applied Mathematics | Computer Sciences | Statistics and Probability

Abstract

Recently there are a considerable amount of work devoted to the study of the algorithmic stability as well as differential privacy (DP) for stochastic gradient methods (SGM). However, most of the existing work focus on the empirical risk minimization (ERM) and the population risk minimization problems. In this paper, we study two types of optimization problems that enjoy wide applications in modern machine learning, namely the minimax problem and the pairwise learning problem.

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