12 11 Learning Rate Scheduling Dive Into Deep Learning 1 0 0 Beta0

So far we primarily focused on optimization algorithms for how to update the weight vectors rather than on the rate at which they are being updated. Nonetheless, adjusting the learning rate is often just as important as the actual algorithm. There are a number of aspects to consider: Most obviously the magnitude of the learning rate matters. If it is too large, optimization diverges, if it is too small, it takes too long to train or we end up with a suboptimal result. We saw previously that the condition number of the problem matters (see e.g., Section 12.6 for details).

Intuitively it is the ratio of the amount of change in the least sensitive direction vs. the most sensitive one. Secondly, the rate of decay is just as important. If the learning rate remains large we may simply end up bouncing around the minimum and thus not reach optimality. Section 12.5 discussed this in some detail and we analyzed performance guarantees in Section 12.4. In short, we want the rate to decay, but probably more slowly than \(\mathcal{O}(t^{-\frac{1}{2}})\) which would be a good choice for convex problems.

Another aspect that is equally important is initialization. This pertains both to how the parameters are set initially (review Section 5.4 for details) and also how they evolve initially. This goes under the moniker of warmup, i.e., how rapidly we start moving towards the solution initially. Large steps in the beginning might not be beneficial, in particular since the initial set of parameters is random. The initial update directions might be quite meaningless, too. Lastly, there are a number of optimization variants that perform cyclical learning rate adjustment.

This is beyond the scope of the current chapter. We recommend the reader to review details in Izmailov et al. (2018), e.g., how to obtain better solutions by averaging over an entire path of parameters. A Gentle Introduction to Learning Rate SchedulersImage by Author | ChatGPT Ever wondered why your neural network seems to get stuck during training, or why it starts strong but fails to reach its full potential? The culprit might be your learning rate – arguably one of the most important hyperparameters in machine learning.

While a fixed learning rate can work, it often leads to suboptimal results. Learning rate schedulers offer a more dynamic approach by automatically adjusting the learning rate during training. In this article, you’ll discover five popular learning rate schedulers through clear visualizations and hands-on examples. You’ll learn when to use each scheduler, see their behavior patterns, and understand how they can improve your model’s performance. We’ll start with the basics, explore sklearn’s approach versus deep learning requirements, then move to practical implementation using the MNIST dataset. By the end, you’ll have both the theoretical understanding and practical code to start using learning rate schedulers in your own projects.

Imagine you’re hiking down a mountain in thick fog, trying to reach the valley. The learning rate is like your step size – take steps too large, and you might overshoot the valley or bounce between mountainsides. Take steps too small, and you’ll move painfully slowly, possibly getting stuck on a ledge before reaching the bottom. In the realm of deep learning, PyTorch stands as a beacon, illuminating the path for researchers and practitioners to traverse the complex landscapes of artificial intelligence. Its dynamic computational graph and user-friendly interface have solidified its position as a preferred framework for developing neural networks. As we delve into the nuances of model training, one essential aspect that demands meticulous attention is the learning rate.

To navigate the fluctuating terrains of optimization effectively, PyTorch introduces a potent ally—the learning rate scheduler. This article aims to demystify the PyTorch learning rate scheduler, providing insights into its syntax, parameters, and indispensable role in enhancing the efficiency and efficacy of model training. PyTorch, an open-source machine learning library, has gained immense popularity for its dynamic computation graph and ease of use. Developed by Facebook's AI Research lab (FAIR), PyTorch has become a go-to framework for building and training deep learning models. Its flexibility and dynamic nature make it particularly well-suited for research and experimentation, allowing practitioners to iterate swiftly and explore innovative approaches in the ever-evolving field of artificial intelligence. At the heart of effective model training lies the learning rate—a hyperparameter crucial for controlling the step size during optimization.

PyTorch provides a sophisticated mechanism, known as the learning rate scheduler, to dynamically adjust this hyperparameter as the training progresses. The syntax for incorporating a learning rate scheduler into your PyTorch training pipeline is both intuitive and flexible. At its core, the scheduler is integrated into the optimizer, working hand in hand to regulate the learning rate based on predefined policies. The typical syntax for implementing a learning rate scheduler involves instantiating an optimizer and a scheduler, then stepping through epochs or batches, updating the learning rate accordingly. The versatility of the scheduler is reflected in its ability to accommodate various parameters, allowing practitioners to tailor its behavior to meet specific training requirements. The importance of learning rate schedulers becomes evident when considering the dynamic nature of model training.

As models traverse complex loss landscapes, a fixed learning rate may hinder convergence or cause overshooting. Learning rate schedulers address this challenge by adapting the learning rate based on the model's performance during training. This adaptability is crucial for avoiding divergence, accelerating convergence, and facilitating the discovery of optimal model parameters. The provided test accuracy of approximately 95.6% suggests that the trained neural network model performs well on the test set. © 2025 ApX Machine LearningEngineered with @keyframes heartBeat { 0%, 100% { transform: scale(1); } 25% { transform: scale(1.3); } 50% { transform: scale(1.1); } 75% { transform: scale(1.2); } } Part of the traditional machine learning recipe is to decay our learning rate (LR) over time.

This ensures that we get fast learning early on, but can get that last push of performance near the edge. Let’s see how much this matters, and if we can get away without it. In classical optimization theory, learning rate must decay for us to get certain convergence guarantees. The intution is that if we stay at a constant learning rate forever, we’ll end up bouncing around the optimum and won’t converge to the exact point. By decaying the change to zero, we will eventually converge to a fixed point at minimum loss. Of course, it’s one thing for a technique to be theoretically sound, and other for it to work in practice…

Let’s try out some differnt learning rate schedules on neural networks. We’ll use the CIFAR-10 dataset this time, which is a set of 50,000 colored images and 10 classes. We’ll use a small vision transformer as our network, and the Adam optimizer as a base. Learning rate decay consistently helps. As as baseline, the blue ‘Constant LR’ curve shows us what happens when we just use a fixed learning rate. The network is still improving, and there’s definitely progress being made at every step.

However, we get a consistent gain from using linear decay, where we simply scale the LR down linearly until it reaches zero at the end of training. The base learning rate (0.001) was found by doing a sweep. So, it is not a problem of having too high of a learning rate throughout training. When it comes to training deep neural networks, one of the crucial factors that significantly influences model performance is the learning rate. The learning rate determines the size of the steps taken during the optimization process and plays a pivotal role in determining how quickly or slowly a model converges to the optimal solution. In recent years, adaptive learning rate scheduling techniques have gained prominence for their effectiveness in optimizing the training process and improving model performance.

Before delving into adaptive learning rate scheduling, let’s first understand why the learning rate is so important in training deep neural networks. In essence, the learning rate controls the amount by which we update the parameters of the model during each iteration of the optimization algorithm, such as stochastic gradient descent (SGD) or its variants. You can run the code for this section in this jupyter notebook link. Code for step-wise learning rate decay at every epoch Code for step-wise learning rate decay at every 2 epoch Code for step-wise learning rate decay at every epoch with larger gamma

Code for reduce on loss plateau learning rate decay of factor 0.1 and 0 patience The learning rate is arguably the most critical hyperparameter in deep learning training, directly influencing how quickly and effectively your neural network converges to optimal solutions. While many practitioners start with a fixed learning rate, implementing dynamic learning rate schedules can dramatically improve model performance, reduce training time, and prevent common optimization pitfalls. This comprehensive guide explores the fundamental concepts, popular scheduling strategies, and practical implementation considerations for learning rate schedules in deep learning training. Before diving into scheduling strategies, it’s essential to understand why the learning rate matters so much in neural network optimization. The learning rate determines the step size during gradient descent, controlling how much the model’s weights change with each training iteration.

A learning rate that’s too high can cause the optimizer to overshoot optimal solutions, leading to unstable training or divergence. Conversely, a learning rate that’s too low results in painfully slow convergence and may trap the model in local minima. The challenge lies in finding the optimal learning rate, which often changes throughout the training process. Early in training, when the model is far from optimal solutions, a higher learning rate can accelerate progress. As training progresses and the model approaches better solutions, a lower learning rate helps fine-tune the weights and achieve better convergence. This dynamic nature of optimal learning rates forms the foundation for learning rate scheduling.

Step decay represents one of the most straightforward and widely-used learning rate scheduling techniques. This method reduces the learning rate by a predetermined factor at specific training epochs or steps. The typical implementation involves multiplying the current learning rate by a decay factor (commonly 0.1 or 0.5) every few epochs. For example, you might start with a learning rate of 0.01 and reduce it by a factor of 10 every 30 epochs. This approach works particularly well for image classification tasks and has been successfully employed in training many landmark architectures like ResNet and VGG networks.

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