2018/08/10 by Li Shen, Shen, Li, Congliang Chen +9 · 3 citations
Computer Science · #FOS: Computer and information sciences #FOS: Mathematics #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Machine Learning and ELM #Neural Networks and Applications #Numerical Analysis (math.NA) #Optimization and Control (math.OC) #Stochastic Gradient Optimization Techniques
paper · pdf · doi:10.48550/arxiv.1808.03408
openalex publication_date 2018/08/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Integrating adaptive learning rate and momentum techniques into SGD leads to a large class of efficiently accelerated adaptive stochastic algorithms, such as AdaGrad, RMSProp, Adam, AccAdaGrad, etc. In spite of their effectiveness in practice, there is still a large gap in their theories of convergences, especially in the difficult non-convex stochastic setting. To fill this gap, we propose weighted AdaGrad with unified momentum, dubbed AdaUSM, which has the main characteristics that (1) it incorporates a unified momentum scheme which covers both the heavy ball momentum and the Nesterov accelerated gradient momentum; (2) it adopts a novel weighted adaptive learning rate that can unify the learning rates of AdaGrad, AccAdaGrad, Adam, and RMSProp. Moreover, when we take polynomially growing weights in AdaUSM, we obtain its O(log(T)/√(T)) convergence rate in the non-convex stochastic setting. We also show that the adaptive learning rates of Adam and RMSProp correspond to taking exponentially growing weights in AdaUSM, thereby providing a new perspective for understanding Adam and RMSProp. Lastly, comparative experiments of AdaUSM against SGD with momentum, AdaGrad, AdaEMA, Adam, and AMSGrad on various deep learning models and datasets are also carried out.