2019/12/31 by Huizhuo Yuan, Yuan, Huizhuo, Xiangru Lian +3 · 1 citation
Computer Science · Engineering · #FOS: Computer and information sciences #FOS: Mathematics #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Machine Learning and ELM #Optimization and Control (math.OC) #Sparse and Compressive Sensing Techniques #Stochastic Gradient Optimization Techniques
paper · pdf · doi:10.48550/arxiv.1912.13515
openalex publication_date 2019/12/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Stochastic compositional optimization arises in many important machine learning tasks such as value function evaluation in reinforcement learning and portfolio management. The objective function is the composition of two expectations of stochastic functions, and is more challenging to optimize than vanilla stochastic optimization problems. In this paper, we investigate the stochastic compositional optimization in the general smooth non-convex setting. We employ a recently developed idea of Stochastic Recursive Gradient Descent to design a novel algorithm named SARAH-Compositional, and prove a sharp Incremental First-order Oracle (IFO) complexity upper bound for stochastic compositional optimization: O((n+m)1/2 ε-2) in the finite-sum case and O(ε-3) in the online case. Such a complexity is known to be the best one among IFO complexity results for non-convex stochastic compositional optimization, and is believed to be optimal. Our experiments validate the theoretical performance of our algorithm.