Mathematical Foundations of Machine Learning

Advancements in Optimization Algorithms and Data Privacy

Abstract

This paper discusses the interdisciplinary research that contributes significantly to theoretical advancements and practical applications in machine learning. It focuses on the mathematical foundations of
machine learning, specifically optimization algorithms and data privacy. The research aims to address the challenges of optimizing machine learning models and ensuring data privacy, particularly in the growing complexity of models. The authors develop novel optimization techniques, such as Accelerated Stochastic Gradient Descent (ASGD) and Robust Adaptive Gradient (RAG), and provide rigorous proofs for their convergence and robustness. They also investigate differential privacy mechanisms, such as Laplace and Gaussian mechanisms, and integrate them into machine learning algorithms like Differentially Private Stochastic Gradient Descent (DP-SGD). The research shows improved convergence rates and robustness compared to traditional techniques, and the differential privacy mechanisms offer strong privacy guarantees while maintaining model utility. These contributions are crucial for the deployment of secure and efficient machine learning systems across various industries, including healthcare, finance, and social media.