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A new regret analysis for Adam-type algorithms

Ahmet Alacaoglu · Yura Malitsky · Panayotis Mertikopoulos · Volkan Cevher

Keywords: [ Convex Optimization ] [ Optimization ] [ Optimization - Convex ]

Abstract: 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 $\beta_{1}$ (typically between $0.9$ and $0.99$). In theory, regret guarantees for online convex optimization require a rapidly decaying $\beta_{1}\to0$ 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 $\beta_{1}$, without further assumptions. We also demonstrate the flexibility of our analysis on a wide range of different algorithms and settings.

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