  Momentum-based acceleration of stochastic gradient descent (SGD) is widely
used in deep learning. We propose the quasi-hyperbolic momentum algorithm (QHM)
as an extremely simple alteration of momentum SGD, averaging a plain SGD step
with a momentum step. We describe numerous connections to and identities with
other algorithms, and we characterize the set of two-state optimization
algorithms that QHM can recover. Finally, we propose a QH variant of Adam
called QHAdam, and we empirically demonstrate that our algorithms lead to
significantly improved training in a variety of settings, including a new
state-of-the-art result on WMT16 EN-DE. We hope that these empirical results,
combined with the conceptual and practical simplicity of QHM and QHAdam, will
spur interest from both practitioners and researchers. Code is immediately
available.
