Adaptive Gradient Methods with Dynamic Bound of Learning Rate
(1902.09843v1)
Published 26 Feb 2019 in cs.LG and stat.ML
Abstract: Adaptive optimization methods such as AdaGrad, RMSprop and Adam have been proposed to achieve a rapid training process with an element-wise scaling term on learning rates. Though prevailing, they are observed to generalize poorly compared with SGD or even fail to converge due to unstable and extreme learning rates. Recent work has put forward some algorithms such as AMSGrad to tackle this issue but they failed to achieve considerable improvement over existing methods. In our paper, we demonstrate that extreme learning rates can lead to poor performance. We provide new variants of Adam and AMSGrad, called AdaBound and AMSBound respectively, which employ dynamic bounds on learning rates to achieve a gradual and smooth transition from adaptive methods to SGD and give a theoretical proof of convergence. We further conduct experiments on various popular tasks and models, which is often insufficient in previous work. Experimental results show that new variants can eliminate the generalization gap between adaptive methods and SGD and maintain higher learning speed early in training at the same time. Moreover, they can bring significant improvement over their prototypes, especially on complex deep networks. The implementation of the algorithm can be found at https://github.com/Luolc/AdaBound .
Adaptive Gradient Methods with Dynamic Bounds on Learning Rate
The paper introduces variants of the Adam and AMSGrad optimization algorithms, named AdaBound and AMSBound, which employ dynamically bounded learning rates to improve convergence and generalization. This work addresses the shortcomings of popular adaptive methods that, while delivering fast initial training, often underperform in terms of generalization compared to non-adaptive methods like stochastic gradient descent (Sgd).
Motivation and Approach
Adaptive optimization methods such as AdaGrad, RMSprop, and Adam adjust learning rates based on the history of gradients, which can result in unstable, extreme learning rates leading to poor generalization and convergence issues. Although AMSGrad was introduced to handle these deficiencies, its performance gains are modest, leaving a significant gap compared to Sgd. Upon empirical examination, the authors identify that extreme learning rates—particularly small ones—at the end of training contribute significantly to poor performance.
To address this, the authors propose AdaBound and AMSBound, which impose dynamic bounds on the learning rates. The algorithms start with bounds allowing for adaptive behavior and gradually shrink them to a fixed constant as training progresses, essentially transitioning from adaptive methods to a behavior akin to Sgd. This dynamic bounding improves convergence characteristics, retaining the initial benefits of fast adaptive learning while eventually stabilizing to leverage the generalization strengths of Sgd.
Theoretical and Empirical Validation
The authors provide theoretical proofs demonstrating the convergence of AdaBound in the convex setting, ensuring that regret is bounded by O(T). They apply similar theoretical constructs to AMSBound, confirming analogous guarantees. These proofs detail how dynamic bounds help mitigate the adverse effects of extreme learning rates, guiding the optimization process more effectively towards optimal solutions.
Empirically, the authors illustrate the efficacy of their methods through experiments on image classification tasks using DenseNet and ResNet on CIFAR-10, as well as LLMing tasks on Penn Treebank using LSTM networks. Across these applications, AdaBound and AMSBound demonstrate superior generalization and competitive or superior test accuracy compared to both classical Sgd and traditional adaptive methods. Notably, the proposed methods particularly excel in deep, complex network structures, where extreme learning rates are more prevalent.
Implications and Future Directions
This research contributes to a deeper understanding of the impact of learning rate dynamics on generalization. By implementing a gradual transition from adaptive methods to Sgd-like behavior, the authors provide a strategy that balances rapid learning with robust generalization. The implications of these results are significant, particularly for deep learning applications where model complexities often lead to intricate gradient behaviors.
The paper also sets the stage for future work exploring other continuous methodologies to transform adaptive methods to Sgd. Additionally, understanding why Sgd consistently shows strong generalization across diverse tasks remains a pertinent avenue for exploration. Finally, further research might refine the bounding functions or find novel approaches to optimize convergence targets in complex models without intensive hyperparameter tuning.
In conclusion, the paper presents a compelling modification to existing optimization algorithms that judiciously controls learning rate dynamics, offering a promising solution to the generalization challenges faced by adaptive gradient methods.