ϵ-Approximation of Adaptive Leaning Rate Optimization Algorithms for Constrained Nonconvex Stochastic Optimization

This brief considers constrained nonconvex stochastic finite-sum and online optimization in deep neural networks. Adaptive-learning-rate optimization algorithms (ALROAs), such as Adam, AMSGrad, and their variants, have widely been used for these optimizations because they are powerful and useful in theory and practice. Here, it is shown that the ALROAs are
$\epsilon $
-approximations for these optimizations. We provide the learning rates, mini-batch sizes, number of iterations, and stochastic gradient complexity with which to achieve
$\epsilon $
-approximations of the algorithms.