A new regret analysis for Adam-type algorithms
Ahmet Alacaoglu,u00a0Yura Malitsky,u00a0Panayotis Mertikopoulos,u00a0Volkan Cevher
In this paper, we focus on a theory-practice gap for Adam and its variants (AMSGrad, AdamNC, etc.). In practice, these algorithms are used with a constant first-order moment parameter $eta_{1}$ (typically between $0.9$ and $0.99$). In theory, regret guarantees for online convex optimization require a rapidly decaying $eta_{1} o0$ schedule. We show that this is an artifact of the standard analysis, and we propose a novel framework that allows us to derive optimal, data-dependent regret bounds with a constant $eta_{1}$, without further assumptions. We also demonstrate the flexibility of our analysis on a wide range of different algorithms and settings.
