Stochastic Three-Composite Convex Minimization

Abstract

We propose a stochastic optimization method for the minimization of the sum of three convex functions, one of which has Lipschitz continuous gradient as well as restricted strong convexity. Our approach is most suitable in the setting where it is computationally advantageous to process smooth term in the decomposition with its stochastic gradient estimate and the other two functions separately with their proximal operators, such as doubly regularized empirical risk minimization problems. We prove the convergence characterization of the proposed algorithm in expectation under the standard assumptions for the stochastic gradient estimate of the smooth term. Our method operates in the primal space and can be considered as a stochastic extension of the three-operator splitting method. Numerical evidence supports the effectiveness of our method in real-world problems.

NIPS 2016

Cited by in corpus (7)

• Dualize, Split, Randomize: Toward Fast Nonsmooth Optimization Algorithms
• Stochastic Proximal Langevin Algorithm: Potential Splitting and Nonasymptotic Rates
• A Stochastic Decoupling Method for Minimizing the Sum of Smooth and Non-Smooth Functions
• Three Operator Splitting with Subgradients, Stochastic Gradients, and Adaptive Learning Rates
• Three Operator Splitting with a Nonconvex Loss Function
• Inertial Three-Operator Splitting Method and Applications
• Stochastic Projective Splitting: Solving Saddle-Point Problems with Multiple Regularizers