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Adaptive Inertia: Disentangling the Effects of Adaptive Learning Rate and Momentum
Zeke Xie · Xinrui Wang · Huishuai Zhang · Issei Sato · Masashi Sugiyama

Wed Jul 20 03:30 PM -- 05:30 PM (PDT) @ Hall E #221

Adaptive Moment Estimation (Adam), which combines Adaptive Learning Rate and Momentum, would be the most popular stochastic optimizer for accelerating the training of deep neural networks. However, it is empirically known that Adam often generalizes worse than Stochastic Gradient Descent (SGD). The purpose of this paper is to unveil the mystery of this behavior in the diffusion theoretical framework. Specifically, we disentangle the effects of Adaptive Learning Rate and Momentum of the Adam dynamics on saddle-point escaping and flat minima selection. We prove that Adaptive Learning Rate can escape saddle points efficiently, but cannot select flat minima as SGD does. In contrast, Momentum provides a drift effect to help the training process pass through saddle points, and almost does not affect flat minima selection. This partly explains why SGD (with Momentum) generalizes better, while Adam generalizes worse but converges faster. Furthermore, motivated by the analysis, we design a novel adaptive optimization framework named Adaptive Inertia, which uses parameter-wise adaptive inertia to accelerate the training and provably favors flat minima as well as SGD. Our extensive experiments demonstrate that the proposed adaptive inertia method can generalize significantly better than SGD and conventional adaptive gradient methods.

Author Information

Zeke Xie (The University of Tokyo/RIKEN AIP)

He obtained Ph.D. in machine learning and M.E. both from The University of Tokyo. He was fortunately supervised by Prof. Masashi Sugiyama and Prof. Issei Sato. He was also affiliated with RIKEN AIP during the Ph.D. study. Before that, he obtained Bachelor of Science from University of Science and Technology of China. His research interests generally lies in machine learning, especially including Deep Learning Theory, Imperfect Information Learning, and AI + Science.

Xinrui Wang (The University of Tokyo)
Huishuai Zhang (Microsoft)
Issei Sato (The University of Tokyo)
Masashi Sugiyama (RIKEN / The University of Tokyo)

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