An Adaptive and Momental Bound Method for Stochastic Learning (1910.12249v1)

Abstract: Training deep neural networks requires intricate initialization and careful selection of learning rates. The emergence of stochastic gradient optimization methods that use adaptive learning rates based on squared past gradients, e.g., AdaGrad, AdaDelta, and Adam, eases the job slightly. However, such methods have also been proven problematic in recent studies with their own pitfalls including non-convergence issues and so on. Alternative variants have been proposed for enhancement, such as AMSGrad, AdaShift and AdaBound. In this work, we identify a new problem of adaptive learning rate methods that exhibits at the beginning of learning where Adam produces extremely large learning rates that inhibit the start of learning. We propose the Adaptive and Momental Bound (AdaMod) method to restrict the adaptive learning rates with adaptive and momental upper bounds. The dynamic learning rate bounds are based on the exponential moving averages of the adaptive learning rates themselves, which smooth out unexpected large learning rates and stabilize the training of deep neural networks. Our experiments verify that AdaMod eliminates the extremely large learning rates throughout the training and brings significant improvements especially on complex networks such as DenseNet and Transformer, compared to Adam. Our implementation is available at: https://github.com/lancopku/AdaMod

An Exploration of AdaMod: Enhancing Adaptive Learning Rate Methods in Stochastic Learning

In the field of deep learning optimization, adaptive learning rate methods such as Adam, AdaGrad, and RMSProp have become central due to their capacity to adjust learning rates based on historical gradient data. These methods offer an advantage over stochastic gradient descent (SGD) by tailoring updates to specific parameters, thereby potentially accelerating convergence. However, as highlighted by Jianbang Ding et al. in their paper "An Adaptive and Momental Bound Method for Stochastic Learning," these adaptive methods are not devoid of challenges, notably issues related to stability and convergence.

The authors identify a compelling problem inherent in existing adaptive methods, particularly Adam, wherein extremely large learning rates at the onset of training can destabilize the learning process, potentially leading to non-convergence. This observation is substantiated through empirical evidence, where such phenomena disrupt training across various complex neural architectures, including DenseNet and Transformer models. To address this, Ding et al. introduce the Adaptive and Momental Bound (AdaMod) method, designed to mitigate these destabilizing large learning rates by imposing adaptive and momental upper bounds.

Key Contributions of AdaMod

AdaMod innovatively augments the Adam algorithm by integrating exponential moving averages to compute a momental bound for the learning rates themselves. This bound functionally clips exaggerated learning rates, thereby smoothing sudden spikes and maintaining stability throughout the training process. Critically, AdaMod aims to impart "long-term memory" into learning rates, leveraging past gradient information to stabilize updates more effectively.

The empirical evaluation presented in this paper demonstrates AdaMod's efficacy across a range of tasks and architectures. For instance, in neural machine translation tasks on datasets such as IWSLT’14 De-En and WMT’14 En-De, AdaMod, without relying on warmup schemes, outperformed Adam, yielding better BLEU scores. This improvement was similarly reflected in image classification tasks on CIFAR-10 and CIFAR-100, where AdaMod provided more consistent and superior performance compared to Adam, particularly in complex networks like DenseNet-121.

Implications and Future Directions

By effectively addressing the stability issues of adaptive learning rates, AdaMod presents a pivotal advancement in stochastic learning methodologies. Its application reduces the dependency on hyperparameter tuning for learning rate scheduling, thereby simplifying the training pipeline across diverse tasks.

Looking forward, one promising direction for AdaMod, as noted by the authors, involves its integration with other stability-enhancing techniques, such as architecture-specific initializations or regularizers. There remains a fascinating avenue to explore the adaptability of AdaMod across even more specialized tasks or in heterogeneous environments where data distribution shifts markedly during training.

Additionally, the balance between stability and convergence speed remains a challenge. While AdaMod shows improvements in generalization and robustness against learning rate initialization, further research might focus on dynamic adjustment of the bounding parameter to capitalize on rapid convergence without sacrificing model robustness.

In summary, the AdaMod method proposed by Ding et al. represents a significant refinement in the adaptive learning rate paradigm, promising enhanced stability and efficiency. It embodies a robust approach to solving some of the foreseen limitations of existing adaptive methods, with substantial implications for deep learning practice and research.