Understanding Adam Optimizer via Online Learning of Updates: Adam is
  FTRL in Disguise
Kwangjun Ahn Zhiyu Zhang Yunbum Kook Yan Dai
Despite the success of the Adam optimizer in practice, the theoretical
understanding of its algorithmic components still remains limited. In
particular, most existing analyses of Adam show the convergence rate that can
be simply achieved by non-adative algorithms like SGD. In this work, we provide
a different perspective based on online learning that underscores the
importance of Adam's algorithmic components. Inspired by Cutkosky et al.
(2023), we consider the framework called online learning of updates, where we
choose the updates of an optimizer based on an online learner. With this
framework, the design of a good optimizer is reduced to the design of a good
online learner. Our main observation is that Adam corresponds to a principled
online learning framework called Follow-the-Regularized-Leader (FTRL). Building
on this observation, we study the benefits of its algorithmic components from
the online learning perspective.