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arXiv · 2305.05675

UAdam: Unified Adam-Type Algorithmic Framework for Non-Convex Stochastic Optimization

Yiming Jiang·Jinlan Liu·Dongpo Xu·Danilo P. Mandic
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Abstract

Adam-type algorithms have become a preferred choice for optimisation in the deep learning setting, however, despite success, their convergence is still not well understood. To this end, we introduce a unified framework for Adam-type algorithms (called UAdam). This is equipped with a general form of the second-order moment, which makes it possible to include Adam and its variants as special cases, such as NAdam, AMSGrad, AdaBound, AdaFom, and Adan. This is supported by a rigorous convergence analysis of UAdam in the non-convex stochastic setting, showing that UAdam converges to the neighborhood of stationary points with the rate of $\mathcal{O}(1/T)$. Furthermore, the size of neighborhood decreases as $\beta$ increases. Importantly, our analysis only requires the first-order momentum factor to be close enough to 1, without any restrictions on the second-order momentum factor. Theoretical results also show that vanilla Adam can converge by selecting appropriate hyperparameters, which provides a theoretical guarantee for the analysis, applications, and further developments of the whole class of Adam-type algorithms.

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Yiming Jiang, Jinlan Liu, Dongpo Xu, Danilo P. Mandic. 2023-05-09. UAdam: Unified Adam-Type Algorithmic Framework for Non-Convex Stochastic Optimization. https://doi.org/10.1162/neco_a_01692

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