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

• URL: http://arxiv.org/abs/2305.05675v1
• Date: Tue, 9 May 2023 13:07:03 GMT
• Title: UAdam: Unified Adam-Type Algorithmic Framework for Non-Convex Stochastic Optimization
• Authors: Yiming Jiang, Jinlan Liu, Dongpo Xu, Danilo P. Mandic
• Abstract summary: We introduce a unified framework for Adam-type algorithms (called UAdam) This is equipped with a general form of the second-order moment, such as NAdamBound, AdaFom, and Adan. We show that UAdam converges to the neighborhood of stationary points with the rate of $mathcalO (1/T)$.
• Score: 20.399244578926474
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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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