12 11 Learning Rate Scheduling Dive Into Deep Learning 1 0 3 D2l

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. © 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); } } 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 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. Interactive deep learning book with code, math, and discussions Implemented with PyTorch, NumPy/MXNet, JAX, and TensorFlow Adopted at 500 universities from 70 countries Star You can modify the code and tune hyperparameters to get instant feedback to accumulate practical experiences in deep learning. We offer an interactive learning experience with mathematics, figures, code, text, and discussions, where concepts and techniques are illustrated and implemented with experiments on real data sets. You can discuss and learn with thousands of peers in the community through the link provided in each section.

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