2017/01/31 by Alp Yurtsever, Yurtsever, Alp, Bằng Công Vũ +3 · 5 citations
Computer Science · Decision Sciences · Engineering · #FOS: Mathematics #Optimization and Control (math.OC) #Risk and Portfolio Optimization #Sparse and Compressive Sensing Techniques #Stochastic Gradient Optimization Techniques
paper · pdf · doi:10.48550/arxiv.1701.09033
openalex publication_date 2017/01/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
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.