Adaptive gradient methods such as RMSProp and Adam use exponential moving estimate of the squared gradient to compute adaptive step sizes, achieving better convergence than SGD in face of noisy objectives. However, Adam can have undesirable convergence behaviors due to unstable or extreme adaptive learning rates. Methods such as AMSGrad and AdaBound have been proposed to stabilize the adaptive learning rates of Adam in the later stage of training, but they do not outperform Adam in some practical tasks such as training Transformers \cite{transformer}. In this paper, we propose an adaptive learning rate principle, in which the running mean of squared gradient in Adam is replaced by a weighted mean, with weights chosen to maximize the estimated variance of each coordinate. This results in a faster adaptation to the local gradient variance, which leads to more desirable empirical convergence behaviors than Adam. We prove the proposed algorithm converges under mild assumptions for nonconvex stochastic optimization problems, and demonstrate the improved efficacy of our adaptive averaging approach on machine translation, natural language understanding and large-batch pretraining of BERT. The code is available at https://github.com/zhuchen03/MaxVA.
翻译:RMSProp 和 Adam 等适应性梯度方法使用平方梯度指数移动估计值来计算适应性步数大小,在面对吵闹的目标时比SGD更接近。然而,Adam可能会由于不稳定或极端的适应性学习率而产生不可取的趋同行为。一些方法,如AMSGrad 和 AdaBound 已经提议在培训的后期阶段稳定Adam的适应性学习率,但在培训变异器和变异器等一些实际任务中,这些方法并不比Adam高。我们在此文件中提出了适应性学习率原则,其中亚当的正方梯度运行平均值被加权平均值取代,并选择了加权平均值,以尽量扩大每个坐标的估计差异。这导致更快地适应当地梯度差异,从而导致比Adam更可取的经验趋同行为。我们证明拟议的算法在非convex 蒸气优化问题的温和假设下趋于一致,并表明我们在机器翻译、自然语言理解和大批前训练BERTERT的适应性平均法方法的效能有所提高。代码可在 https://gthhuthub.comzchan03/zchan03/MVA03/MA03。