- Hybrid Stochastic Gradient Descent Algorithms forStochastic Nonconvex Optimization Quoc Tran-Dinh(quoctdemail.unc.edu) H. Nhan Pham(nhanphlive.unc.edu) T. Dzung Phan(phanduus.ibm.com) M. Lam Nguyen(LamNguyen.MLTDibm.com) Abstract: We introduce a hybrid stochastic estimator to design stochastic gradient algorithms for solving stochastic optimization problems. Such a hybrid estimator is a convex combination of two existing biased and unbiased estimators and leads to some useful property on its variance. We limit our consideration to a hybrid SARAH-SGD for nonconvex expectation problems. However, our idea can be extended to handle a broader class of estimators in both convex and nonconvex settings. We propose a new single-loop stochastic gradient descent algorithm that can achieve $O(\max\{\sigma^3\varepsilon^{-1},\sigma\varepsilon^{-3}\})$-complexity bound to obtain an $\varepsilon$-stationary point under smoothness and $\sigma^2$-bounded variance assumptions. This complexity is better than $O(\sigma^2\varepsilon^{-4})$ often obtained in state-of-the-art SGDs when $\sigma < O(\varepsilon^{-3})$. We also consider different extensions of our method, including constant and adaptive step-size with single-loop, double-loop, and mini-batch variants. We compare our algorithms with existing methods on several datasets using two nonconvex models. Keywords: Stochastic Optimization; Nonconvex Optimization; Hybrid Gradient Descent Category 1: Nonlinear Optimization Category 2: Stochastic Programming Citation: This is a preprint. Download: [PDF]Entry Submitted: 05/28/2019Entry Accepted: 05/28/2019Entry Last Modified: 05/28/2019Modify/Update this entry Visitors Authors More about us Links Subscribe, Unsubscribe Digest Archive Search, Browse the Repository Submit Update Policies Coordinator's Board Classification Scheme Credits Give us feedback Optimization Journals, Sites, Societies Optimization Online is supported by the Mathematical Optmization Society.