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Learning Rate Scheduling Cosine Vs Linear Vs Exponential Decay For

Leo Migdal
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learning rate scheduling cosine vs linear vs exponential decay for

Neural network training fails when learning rates stay constant throughout epochs. Static learning rates cause slow convergence or unstable training dynamics. Learning rate scheduling solves this problem by adjusting rates during training. This guide compares three popular scheduling methods: cosine decay, linear decay, and exponential decay. You'll learn implementation details, performance characteristics, and selection criteria for each approach. Learning rate scheduling dynamically adjusts the learning rate during neural network training.

The scheduler reduces learning rates as training progresses, allowing models to converge more effectively. Key benefits of learning rate scheduling: Cosine decay follows a cosine curve pattern, starting high and gradually decreasing to zero. This smooth transition provides excellent convergence properties for deep learning models. When training a machine learning model, the learning rate plays a important role in determining how quickly the model adjusts its weights based on the errors it makes. If we start with a learning rate that's too high, the model might learn quickly but could overshoot the best solution.

If it's too low, learning can become too slow and the model might get stuck before reaching an optimal solution. To address this learning rate decay was introduced which helps us adjust the learning rate during training. We start with a higher rate which allows the model to make larger updates and learn faster. As training progresses and the model gets closer to an optimal solution, the learning rate decreases allowing for finer adjustments and better convergence. Learning rate decay works similarly to driving toward a parking spot. Initially, we drive fast to cover more distance quickly but as we get closer to our destination, we slow down to park more accurately.

In machine learning, this concept translates to starting with a larger learning rate to make faster progress in the beginning and then gradually reducing it to fine-tune the model’s weights in the later stages... The decay is designed to allow the model to make large, broad adjustments early in training and more delicate adjustments as it approaches the optimal solution. This controlled approach helps the model converge more efficiently without overshooting or getting stuck. There are several methods to implement learning rate decay each with a different approach to how the learning rate decreases over time. Some methods decrease the learning rate in discrete steps while others reduce it more smoothly. The choice of decay method can depend on the task, model and how quickly the learning rate needs to be reduced during training.

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. 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. © 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); } } Learning rate is one of the most important hyperparameters in the training of neural networks, impacting the speed and effectiveness of the learning process. A learning rate that is too high can cause the model to oscillate around the minimum, while a learning rate that is too low can cause the training process to be very slow or... This article provides a visual introduction to learning rate schedulers, which are techniques used to adapt the learning rate during training. In the context of machine learning, the learning rate is a hyperparameter that determines the step size at which an optimization algorithm (like gradient descent) proceeds while attempting to minimize the loss function.

Now, let’s move on to learning rate schedulers. A learning rate scheduler is a method that adjusts the learning rate during the training process, often lowering it as the training progresses. This helps the model to make large updates at the beginning of training when the parameters are far from their optimal values, and smaller updates later when the parameters are closer to their optimal... Several learning rate schedulers are widely used in practice. In this article, we will focus on three popular ones:

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