Learning Rate Scheduling An Alchemist S Notes On Deep Learning

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. 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. 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. When training neural networks, one of the most critical hyperparameters is the learning rate (η). It controls how much the model updates its parameters in response to the computed gradient during optimization. Choosing the right learning rate is crucial for achieving optimal model performance, as it directly affects convergence speed, stability, and the generalization ability of the network. The learning rate determines how quickly or slowly a neural network learns from data.

It plays a key role in finding the optimal set of weights that minimize the loss function. A well-chosen learning rate ensures: Choosing an inappropriate learning rate can lead to several issues: The learning rate (η) is a fundamental hyperparameter in gradient-based optimization methods like Stochastic Gradient Descent (SGD) and its variants. It determines the step size in updating the model parameters (θ) during training. The standard gradient descent algorithm updates model parameters using the following formula:

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 11.6 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 11.5 discussed this in some detail and we analyzed performance guarantees in Section 11.4. 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 4.8 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. Sarah Lee AI generated Llama-4-Maverick-17B-128E-Instruct-FP8 6 min read · June 10, 2025 Deep learning models are notoriously sensitive to the choice of hyperparameters, and the learning rate is one of the most critical hyperparameters to tune. A well-designed learning rate schedule can significantly improve the convergence rate and overall performance of a deep learning model. In this article, we will explore advanced techniques for learning rate scheduling, including warm restarts and cyclical learning rates.

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