A new regret analysis for Adam-type algorithms

Ahmet Alacaoglu; Yura Malitsky; Panayotis Mertikopoulos; Volkan Cevher

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arXiv · 2003.09729

A new regret analysis for Adam-type algorithms

Ahmet Alacaoglu·Yura Malitsky·Panayotis Mertikopoulos·Volkan Cevher

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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 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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BibTeX RIS

Ahmet Alacaoglu, Yura Malitsky, Panayotis Mertikopoulos, Volkan Cevher. 2020-03-21. A new regret analysis for Adam-type algorithms. https://arxiv.org/abs/2003.09729

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