2021/10/07 by Alp Yurtsever, Alex Gu, Yurtsever, Alp +3 · 3 citations
Computer Science · Engineering · #FOS: Mathematics #Machine Learning and Algorithms #Machine Learning and ELM #Optimization and Control (math.OC) #Sparse and Compressive Sensing Techniques #Stochastic Gradient Optimization Techniques
paper · pdf · doi:10.48550/arxiv.2110.03274
openalex publication_date 2021/10/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Three Operator Splitting (TOS) (Davis & Yin, 2017) can minimize the sum of multiple convex functions effectively when an efficient gradient oracle or proximal operator is available for each term. This requirement often fails in machine learning applications: (i) instead of full gradients only stochastic gradients may be available; and (ii) instead of proximal operators, using subgradients to handle complex penalty functions may be more efficient and realistic. Motivated by these concerns, we analyze three potentially valuable extensions of TOS. The first two permit using subgradients and stochastic gradients, and are shown to ensure a O(1/√(t)) convergence rate. The third extension AdapTOS endows TOS with adaptive step-sizes. For the important setting of optimizing a convex loss over the intersection of convex sets AdapTOS attains universal convergence rates, i.e., the rate adapts to the unknown smoothness degree of the objective. We compare our proposed methods with competing methods on various applications.