An improvement of the convergence proof of the ADAM-Optimizer
This work addresses a theoretical gap for researchers and practitioners relying on ADAM's convergence guarantees, but it is incremental as it fixes an existing proof rather than introducing new methods.
The paper identifies mistakes in the original convergence proof of the ADAM optimizer and provides an improved proof to correct these errors.
A common way to train neural networks is the Backpropagation. This algorithm includes a gradient descent method, which needs an adaptive step size. In the area of neural networks, the ADAM-Optimizer is one of the most popular adaptive step size methods. It was invented in \cite{Kingma.2015} by Kingma and Ba. The $5865$ citations in only three years shows additionally the importance of the given paper. We discovered that the given convergence proof of the optimizer contains some mistakes, so that the proof will be wrong. In this paper we give an improvement to the convergence proof of the ADAM-Optimizer.