AdaMod

2000년 도입 · 논문 1편에서 사용

AdaMod is a stochastic optimizer that restricts adaptive learning rates with adaptive and momental upper bounds. The dynamic learning rate bounds are based on the exponential moving averages of the adaptive learning rates themselves, which smooth out unexpected large learning rates and stabilize the training of deep neural networks. The weight updates are performed as: $$ g\_{t} = \nabla{f}\_{t}\left(\theta\_{t-1}\right) $$ $$ m\_{t} = \beta\_{1}m\_{t-1} + \left(1-\beta\_{1}\right)g\_{t} $$ $$ v\_{t} = \beta\_{2}v\_{t-1} + \left(1-\beta\_{2}\right)g\_{t}^{2} $$ $$ \hat{m}\_{t} = m\_{t} / \left(1 - \beta^{t}\_{1}\right)$$ $$ \hat{v}\_{t} = v\_{t} / \left(1 - \beta^{t}\_{2}\right)$$ $$ \eta\_{t} = \alpha\_{t} / \left(\sqrt{\hat{v}\_{t}} + \epsilon\right) $$ $$ s\_{t} = \beta\_{3}s\_{t-1} + (1-\beta\_{3})\eta\_{t} $$ $$ \hat{\eta}\_{t} = \text{min}\left(\eta\_{t}, s\_{t}\right) $$ $$ \theta\_{t} = \theta\_{t-1} - \hat{\eta}\_{t}\hat{m}\_{t} $$

출처: An Adaptive and Momental Bound Method for Stochastic Learning

소개 논문: An Adaptive and Momental Bound Method for Stochastic Learning