Jul 12, 2020
Stochastic gradient methods with momentum are widely used in applications and at the core of optimization subroutines in many popular machine learning libraries. However, their sample complexities have never been obtained for problems that are non-convex and non-smooth. This paper establishes the convergence rate of a stochastic subgradient method with a momentum term of Polyak type for a broad class of non-smooth, non-convex, and constrained optimization problems. Our key innovation is the construction of a special Lyapunov function for which the proven complexity can be achieved without any tunning of the momentum parameter. For smooth problems, we extend the known complexity bound to the constrained case and demonstrate how the unconstrained case can be analyzed under weaker assumptions than the state-of-the art. Numerical results confirm our theoretical developments.
The International Conference on Machine Learning (ICML) is the premier gathering of professionals dedicated to the advancement of the branch of artificial intelligence known as machine learning. ICML is globally renowned for presenting and publishing cutting-edge research on all aspects of machine learning used in closely related areas like artificial intelligence, statistics and data science, as well as important application areas such as machine vision, computational biology, speech recognition, and robotics. ICML is one of the fastest growing artificial intelligence conferences in the world. Participants at ICML span a wide range of backgrounds, from academic and industrial researchers, to entrepreneurs and engineers, to graduate students and postdocs.
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