Variance Reduction on Adaptive Stochastic Mirror Descent

We study the idea of variance reduction applied to adaptive stochastic mirror descent algorithms in nonsmooth nonconvex finite-sum optimization problems. We propose a simple yet generalized adaptive mirror descent algorithm with variance reduction named SVRAMD and provide its convergence analysis in different settings. We prove that variance reduction reduces the gradient complexity of most adaptive mirror descent algorithms and boost their convergence. In particular, our general theory implies variance reduction can be applied to algorithms using time-varying step sizes and self-adaptive algorithms such as AdaGrad and RMSProp. Moreover, our convergence rates recover the best existing rates of non-adaptive algorithms. We check the validity of our claims using experiments in deep learning.Comment: NeurIPS 2020 OPT worksho

The Effect of Temperature and Strain Rate on the Interfacial Behavior of Glass Fiber Reinforced Polypropylene Composites: A Molecular Dynamics Study

To make better use of fiber reinforced polymer composites in automotive applications, a clearer knowledge of its interfacial properties under dynamic and thermal loadings is necessary. In the present study, the interfacial behavior of glass fiber reinforced polypropylene (PP) composites under different loading temperatures and strain rates were investigated via molecular dynamics simulation. The simulation results reveal that PP molecules move easily to fit tensile deformation at higher temperatures, resulting in a lower interfacial strength of glass fiber–PP interface. The interfacial strength is enhanced with increasing strain rate because the atoms do not have enough time to relax at higher strain rates. In addition, the non-bonded interaction energy plays a crucial role during the tensile deformation of composites. The damage evolution of glass fiber–PP interface follows Weibull’s distribution. At elevated temperatures, tensile loading is more likely to cause cohesive failure because the mechanical property of PP is lower than that of the glass fiber–PP interface. However, at higher strain rates, the primary failure mode is interfacial failure because the strain rate dependency of PP is more pronounced than that of the glass fiber–PP interface. The relationship between the failure modes and loading conditions obtained by molecular dynamics simulation is consistent with the author’s previous experimental studies