Katyusha X: Practical Momentum Method for Stochastic Sum-of-Nonconvex Optimization

Abstract

The problem of minimizing sum-of-nonconvex functions (i.e., convex functions that are average of non-convex ones) is becoming increasingly important in machine learning, and is the core machinery for PCA, SVD, regularized Newton's method, accelerated non-convex optimization, and more. We show how to provably obtain an accelerated stochastic algorithm for minimizing sum-of-nonconvex functions, by $\text{adding one additional line}$ to the well-known SVRG method. This line corresponds to momentum, and shows how to directly apply momentum to the finite-sum stochastic minimization of sum-of-nonconvex functions. As a side result, our method enjoys linear parallel speed-up using mini-batch.

References in corpus (2)

• Un-regularizing: approximate proximal point and faster stochastic algorithms for empirical risk minimization
• Finding Linear Structure in Large Datasets with Scalable Canonical Correlation Analysis

Cited by in corpus (8)

• The Practicality of Stochastic Optimization in Imaging Inverse Problems
• Lower Bounds for Smooth Nonconvex Finite-Sum Optimization
• Variance Reduction with Sparse Gradients
• Delayed Projection Techniques for Linearly Constrained Problems: Convergence Rates, Acceleration, and Applications
• On the Convergence of Memory-Based Distributed SGD
• Multiplicative Weights Update as a Distributed Constrained Optimization Algorithm: Convergence to Second-order Stationary Points Almost Always
• ADASS: Adaptive Sample Selection for Training Acceleration
• Tight Lower Complexity Bounds for Strongly Convex Finite-Sum Optimization