Adaptive Inertia: Disentangling the Effects of Adaptive Learning Rate and Momentum

Zeke Xie, Xinrui Wang, Huishuai Zhang, Issei Sato, Masashi Sugiyama
Proceedings of the 39th International Conference on Machine Learning, PMLR 162:24430-24459, 2022.

Abstract

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.

Cite this Paper

BibTeX
@InProceedings{pmlr-v162-xie22d, title = {Adaptive Inertia: Disentangling the Effects of Adaptive Learning Rate and Momentum}, author = {Xie, Zeke and Wang, Xinrui and Zhang, Huishuai and Sato, Issei and Sugiyama, Masashi}, booktitle = {Proceedings of the 39th International Conference on Machine Learning}, pages = {24430--24459}, year = {2022}, editor = {Chaudhuri, Kamalika and Jegelka, Stefanie and Song, Le and Szepesvari, Csaba and Niu, Gang and Sabato, Sivan}, volume = {162}, series = {Proceedings of Machine Learning Research}, month = {17--23 Jul}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v162/xie22d/xie22d.pdf}, url = {https://proceedings.mlr.press/v162/xie22d.html}, abstract = {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.} }
Endnote
%0 Conference Paper %T Adaptive Inertia: Disentangling the Effects of Adaptive Learning Rate and Momentum %A Zeke Xie %A Xinrui Wang %A Huishuai Zhang %A Issei Sato %A Masashi Sugiyama %B Proceedings of the 39th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2022 %E Kamalika Chaudhuri %E Stefanie Jegelka %E Le Song %E Csaba Szepesvari %E Gang Niu %E Sivan Sabato %F pmlr-v162-xie22d %I PMLR %P 24430--24459 %U https://proceedings.mlr.press/v162/xie22d.html %V 162 %X 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.
APA
Xie, Z., Wang, X., Zhang, H., Sato, I. & Sugiyama, M.. (2022). Adaptive Inertia: Disentangling the Effects of Adaptive Learning Rate and Momentum. Proceedings of the 39th International Conference on Machine Learning, in Proceedings of Machine Learning Research 162:24430-24459 Available from https://proceedings.mlr.press/v162/xie22d.html.

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