Learning Rate Optimization in Neural Networks: Challenges and Solutions in Training Dynamics
Ferhat SARIKAYA
MSc. AI and Adaptive Systems — AI Researcher, MLOps Engineer, Big Data Architect
Introduction
One of the most difficult problems in deep learning is finding the appropriate learning rates for learning the neural network. In this comprehensive analysis, we investigate the basic questions related to learning rate choice, their impact on training dynamics, as well as the current approaches. To develop good, robust, efficient training procedures for modern neural networks, one has to understand and effectively manage learning rates.
High Learning Rate Challenges
Convergence of neural networks is notoriously difficult and is often adversely affected by overly high learning rates. High learning rates cause the training process to be unstable, characterised by fast oscillations of the training process around the optimal points. As Bengio's (2012) complete study shows, these oscillations might not allow the model to converge to meaningful solutions. The reason for the phenomenon is simple: large learning rates make the optimization algorithm take steps that are too large (so often overshooting potential minima in the loss landscape).
This problem is further explored by Goodfellow et al. (2016), who show that high learning rates lead to explosive gradient behavior. In other words, it manifests itself by having dramatic spikes in the loss function that demolish the learning process. High learning rates introduce numerical instability that can cause weight updates so large they push the model parameters into regions where the activation functions saturate, rendering gradients vanishing or preventing training from proceeding altogether.
Low Learning Rate Implications
Conversely, when such extremely low learning rates are implemented, they impose an equally detrimental set of problems during training. As shown by Smith (2017), very low learning rates almost lead to the model becoming trapped in high loss plateaus. In this situation, the parameter updates that the model makes are so tiny that it effectively stops training and fails to leave local minima or saddle points of the loss landscape.
Another very important concern is the computational inefficiency brought by low learning rates. This takes training progress to becoming very, very slow, where you need many more epochs than before to see convergence. With this extended training duration, it is not only computationally expensive, but also increases the risk that we will stop training early before we could reach optimal performance levels. Additionally, due to a lack of momentum, the model may not have enough speed to pass through the loss landscape, and thus may become doomed to suboptimal solutions.
Modern Solutions and Optimization Approaches
Learning Rate Scheduling
Sophisticated learning rate scheduling has appeared in contemporary deep learning. Based on that, Loshchilov and Hutter (2016) introduced a stochastic gradient descent with warm restarts (SGDR) that applies a cosine annealing schedule. With these smooth transitions in learning rate adjustments, we ensure that exploration is not too strong, and exploration is not too weak. The cosine annealing schedule, respectively, steps down the learning rate in cosine curve form with occasional restarts at the beginning learning rate to avoid local minimas and explore the other regions in the loss landscape.
Adaptive Optimization Methods
Adaptive learning rate optimizers have been introduced to the field of neural network training, revolutionising it. Kingma and Ba's (2016) Adam optimizer, however, represents a very major breakthrough in this area. Adam combines the benefits of two other optimization techniques: It takes this momentum, which helps to accelerate training along the correct directions, and this RMSprop that optimises the learning rates for different parameters. This combined feature allows the optimizer to work on sparse gradients without unnecessary slowing down of the learning rates, all the while being running for as long as necessary.
Learning Rate Warm-up Strategies
In fact, Goyal et al. (2017) showed how learning rate warm up is crucial, but only in large scale training scenarios. The warm up process is the process of increasing the learning rate from a tiny first value to the target value in several iterations. It also makes the early phases of training more stable when gradients can be especially noisy and bewildering. One of the most valuable aspects of the technique has been in training large models that require large batch sizes, where training stability at the beginning of training is critical to successful convergence.
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Conclusion
Learning rates remain the effective management of the success of neural network training. With the development of modern scheduling techniques, adaptive optimization techniques, and strategic warmup techniques, learning rate problems are now amenable to a robust toolbox of techniques. While the field keeps evolving, we will likely start seeing more sophisticated and more automated approaches to learning rate optimization that can incorporate parts of the neural architecture search and meta learning. With importance, it is necessary to grasp such techniques and to use them effectively so that they can effectively help achieve the best model performance and the best training efficiency in a deep learning environment.
References
[1] Bengio, Y. (2012). Practical Recommendations for Gradient-Based Training of Deep Architectures. In Lecture notes in computer science (pp. 437–478). https://doi.org/10.1007/978-3-642-35289-8_26
[2] Goodfellow, I., Bengio, Y., & Courville, A. (2016). Deep learning. MIT Press.
[3] Goyal, P., Dollár, P., Girshick, R. B., Noordhuis, P., Wesolowski, L., Kyrola, A., Tulloch, A., Jia, Y., & He, K. (2017). Accurate, large minibatch SGD: training ImageNet in 1 hour. arXiv (Cornell University). https://doi.org/10.48550/arxiv.1706.02677
[4] He, K., Zhang, X., Ren, S., & Sun, J. (2016). Deep Residual Learning for Image Recognition. 2016 IEEE Conference on Computer Vision and Pattern Recognition (CVPR). https://doi.org/10.1109/cvpr.2016.90
[5] Kingma, D. P., & Ba, J. L. (2014). Adam: A method for stochastic optimization. arXiv (Cornell University). https://doi.org/10.48550/arxiv.1412.6980
[6] Loshchilov, I., & Hutter, F. (2016). SGDR: Stochastic Gradient Descent with Warm Restarts. arXiv (Cornell University). https://doi.org/10.48550/arxiv.1608.03983
[7] Smith, L. N. (2017). Cyclical Learning Rates for Training Neural Networks (pp. 464–472). 2017 IEEE Winter Conference on Applications of Computer Vision (WACV). https://doi.org/10.1109/wacv.2017.58
[8] Zhang, M. R., Lucas, J., Hinton, G., & Ba, J. (2019). Lookahead Optimizer: k steps forward, 1 step back. In 33rd Conference on Neural Information Processing Systems (NeurIPS 2019), Vancouver, Canada. https://proceedings.neurips.cc/paper_files/paper/2019/file/90fd4f88f588ae64038134f1eeaa023f-Paper.pdf
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