Review Non-convex Optimization Method for Machine Learning

TL;DR

This paper surveys non-convex optimization methods in machine learning, addressing the challenges posed by complex loss landscapes with local minima and saddle points. It covers gradient-based techniques, saddle-point escaping strategies, and non-convex regularization, while highlighting practical approaches to reduce computation through sparsity, subsampling, and pruning. The discussion spans deep neural networks, non-convex SVM losses, matrix factorization, and GANs, illustrating how focusing on good local minima can yield competitive performance with lower compute. The authors also outline future research directions in scalability, landscape understanding, robustness, and emerging domains like reinforcement learning and quantum machine learning.

Abstract

Non-convex optimization is a critical tool in advancing machine learning, especially for complex models like deep neural networks and support vector machines. Despite challenges such as multiple local minima and saddle points, non-convex techniques offer various pathways to reduce computational costs. These include promoting sparsity through regularization, efficiently escaping saddle points, and employing subsampling and approximation strategies like stochastic gradient descent. Additionally, non-convex methods enable model pruning and compression, which reduce the size of models while maintaining performance. By focusing on good local minima instead of exact global minima, non-convex optimization ensures competitive accuracy with faster convergence and lower computational overhead. This paper examines the key methods and applications of non-convex optimization in machine learning, exploring how it can lower computation costs while enhancing model performance. Furthermore, it outlines future research directions and challenges, including scalability and generalization, that will shape the next phase of non-convex optimization in machine learning.