  Optimizer is an essential component for the success of deep learning, which
guides the neural network to update the parameters according to the loss on the
training set. SGD and Adam are two classical and effective optimizers on which
researchers have proposed many variants, such as SGDM and RAdam. In this paper,
we innovatively combine the backward-looking and forward-looking aspects of the
optimizer algorithm and propose a novel \textsc{Admeta} (\textbf{A}
\textbf{D}ouble exponential \textbf{M}oving averag\textbf{E} \textbf{T}o
\textbf{A}daptive and non-adaptive momentum) optimizer framework. For
backward-looking part, we propose a DEMA variant scheme, which is motivated by
a metric in the stock market, to replace the common exponential moving average
scheme. While in the forward-looking part, we present a dynamic lookahead
strategy which asymptotically approaches a set value, maintaining its speed at
early stage and high convergence performance at final stage. Based on this
idea, we provide two optimizer implementations, \textsc{AdmetaR} and
\textsc{AdmetaS}, the former based on RAdam and the latter based on SGDM.
Through extensive experiments on diverse tasks, we find that the proposed
\textsc{Admeta} optimizer outperforms our base optimizers and shows advantages
over recently proposed competitive optimizers. We also provide theoretical
proof of these two algorithms, which verifies the convergence of our proposed
\textsc{Admeta}.
