AdaSAM: Boosting Sharpness-Aware Minimization with Adaptive Learning Rate and Momentum for Training Deep Neural Networks
This provides theoretical guarantees for an optimizer variant that improves training of deep neural networks, but it is incremental as it builds on existing SAM methods.
The paper tackles the problem of analyzing the convergence rate of AdaSAM, an optimizer combining Sharpness-Aware Minimization with adaptive learning rate and momentum, by theoretically proving a convergence rate of O(1/√(bT)) in stochastic non-convex settings and showing it achieves linear speedup with mini-batch size b, with experiments on NLP tasks demonstrating superior performance over SGD, AMSGrad, and SAM.
Sharpness aware minimization (SAM) optimizer has been extensively explored as it can generalize better for training deep neural networks via introducing extra perturbation steps to flatten the landscape of deep learning models. Integrating SAM with adaptive learning rate and momentum acceleration, dubbed AdaSAM, has already been explored empirically to train large-scale deep neural networks without theoretical guarantee due to the triple difficulties in analyzing the coupled perturbation step, adaptive learning rate and momentum step. In this paper, we try to analyze the convergence rate of AdaSAM in the stochastic non-convex setting. We theoretically show that AdaSAM admits a $\mathcal{O}(1/\sqrt{bT})$ convergence rate, which achieves linear speedup property with respect to mini-batch size $b$. Specifically, to decouple the stochastic gradient steps with the adaptive learning rate and perturbed gradient, we introduce the delayed second-order momentum term to decompose them to make them independent while taking an expectation during the analysis. Then we bound them by showing the adaptive learning rate has a limited range, which makes our analysis feasible. To the best of our knowledge, we are the first to provide the non-trivial convergence rate of SAM with an adaptive learning rate and momentum acceleration. At last, we conduct several experiments on several NLP tasks, which show that AdaSAM could achieve superior performance compared with SGD, AMSGrad, and SAM optimizers.