Calibrating the Adaptive Learning Rate to Improve Convergence of ADAM
This work addresses convergence problems in deep learning optimization for researchers and practitioners, offering incremental improvements over existing adaptive gradient methods.
The paper tackles the issue of anisotropic adaptive learning rates in adaptive gradient methods, which can hinder convergence and generalization, by proposing new methods (Sadam and SAMSGrad) that calibrate the learning rate with a softplus function, resulting in improved convergence speed and outperforming existing methods in deep learning tasks.
Adaptive gradient methods (AGMs) have become popular in optimizing the nonconvex problems in deep learning area. We revisit AGMs and identify that the adaptive learning rate (A-LR) used by AGMs varies significantly across the dimensions of the problem over epochs (i.e., anisotropic scale), which may lead to issues in convergence and generalization. All existing modified AGMs actually represent efforts in revising the A-LR. Theoretically, we provide a new way to analyze the convergence of AGMs and prove that the convergence rate of \textsc{Adam} also depends on its hyper-parameter $ε$, which has been overlooked previously. Based on these two facts, we propose a new AGM by calibrating the A-LR with an activation ({\em softplus}) function, resulting in the \textsc{Sadam} and \textsc{SAMSGrad} methods \footnote{Code is available at https://github.com/neilliang90/Sadam.git.}. We further prove that these algorithms enjoy better convergence speed under nonconvex, non-strongly convex, and Polyak-Łojasiewicz conditions compared with \textsc{Adam}. Empirical studies support our observation of the anisotropic A-LR and show that the proposed methods outperform existing AGMs and generalize even better than S-Momentum in multiple deep learning tasks.