Papers › ADOPT: Modified Adam Can Converge with Any β₂ with the Optimal Rate

ADOPT: Modified Adam Can Converge with Any β₂ with the Optimal Rate

5 Nov 2024arXiv:2411.02853archive 2025-07-28

Shohei Taniguchi, Keno Harada, Gouki Minegishi, Yuta Oshima, Seong Cheol Jeong, Go Nagahara, Tomoshi Iiyama, Masahiro Suzuki, Yusuke Iwasawa, Yutaka Matsuo

Adam is one of the most popular optimization algorithms in deep learning. However, it is known that Adam does not converge in theory unless choosing a hyperparameter, i.e., β₂, in a problem-dependent manner. There have been many attempts to fix the non-convergence (e.g., AMSGrad), but they require an impractical assumption that the gradient noise is uniformly bounded. In this paper, we propose a new adaptive gradient method named ADOPT, which achieves the optimal convergence rate of 𝒪 ( 1 / √(T) ) with any choice of β₂ without depending on the bounded noise assumption. ADOPT addresses the non-convergence issue of Adam by removing the current gradient from the second moment estimate and changing the order of the momentum update and the normalization by the second moment estimate. We also conduct intensive numerical experiments, and verify that our ADOPT achieves superior results compared to Adam and its variants across a wide range of tasks, including image classification, generative modeling, natural language processing, and deep reinforcement learning. The implementation is available at https://github.com/iShohei220/adopt.

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Methods

Introduced by this paper: ADOPT

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