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.

本研究针对非凸优化在机器学习中的应用，特别是在深度神经网络和支持向量机等复杂模型中面临的局部极小值和鞍点问题。论文提出通过优化策略降低计算成本，同时确保模型性能，强调关注良好的局部极小值可实现更快的收敛速度和低计算开销，未来的研究将集中于可扩展性和泛化等挑战。

机器学习的非凸优化方法综述