On the Variance of the Adaptive Learning Rate and Beyond
It addresses training instability in adaptive optimizers like Adam, offering a more robust method for deep learning practitioners, though it is incremental as it builds on existing Adam variants.
The paper identifies that adaptive learning rates have high variance early in training, showing warmup reduces this variance, and proposes RAdam to rectify the variance, achieving improved performance in tasks like image classification and language modeling.
The learning rate warmup heuristic achieves remarkable success in stabilizing training, accelerating convergence and improving generalization for adaptive stochastic optimization algorithms like RMSprop and Adam. Here, we study its mechanism in details. Pursuing the theory behind warmup, we identify a problem of the adaptive learning rate (i.e., it has problematically large variance in the early stage), suggest warmup works as a variance reduction technique, and provide both empirical and theoretical evidence to verify our hypothesis. We further propose RAdam, a new variant of Adam, by introducing a term to rectify the variance of the adaptive learning rate. Extensive experimental results on image classification, language modeling, and neural machine translation verify our intuition and demonstrate the effectiveness and robustness of our proposed method. All implementations are available at: https://github.com/LiyuanLucasLiu/RAdam.