Why ADAM Beats SGD for Attention Models	
Authors: Jingzhao Zhang, Sai Praneeth Karimireddy, Andreas Veit, Seungyeon Kim, Sashank J Reddi, Sanjiv Kumar, Suvrit Sra
Keywords: Optimization, ADAM, Deep learning
TL;DR: Adaptive methods provably beat SGD in training attention models due to existence of heavy tailed noise.
Abstract: While stochastic gradient descent (SGD) is still the de facto algorithm in deep learning, adaptive methods like Adam have been observed to outperform SGD across important tasks, such as attention models. The settings under which SGD performs poorly in comparison to Adam are not well understood yet. In this paper, we provide empirical and theoretical evidence that a heavy-tailed distribution of the noise in stochastic gradients is a root cause of SGD's poor performance. Based on this observation, we study clipped variants of SGD that circumvent this issue; we then analyze their convergence under heavy-tailed noise. Furthermore, we develop a new adaptive coordinate-wise clipping algorithm (ACClip) tailored to such settings. Subsequently, we show how adaptive methods like Adam can be viewed through the lens of clipping, which helps us explain Adam's strong performance under heavy-tail noise settings. Finally, we show that the proposed ACClip outperforms Adam for both BERT pretraining and finetuning tasks.