Learning Rate Schedules: Motivation

Optimization algorithms such as Stochastic Gradient Descent (SGD), Momentum, RMSprop, and Adam are frequently used in deep learning. A central component in these algorithms is the learning rate, often denoted as $\alpha$. This hyperparameter controls the step size taken during each parameter update, guiding the descent. The learning rate is commonly treated as a constant value chosen before training begins. However, is a fixed learning rate always the best approach?

Consider the typical progression of model training. Early on, our model's parameters are likely far from their optimal values. The loss surface might be relatively steep or complex in this region. A larger learning rate can be advantageous here, allowing the optimizer to take substantial steps, traverse flat regions quickly, and make rapid progress toward areas with lower loss. Think of it as taking large strides when exploring an expansive, unknown terrain.

However, as training progresses and the parameters get closer to a good solution (a minimum), a large learning rate can become problematic. The optimizer might overshoot the minimum, bouncing back and forth across the valley floor without settling in. This can lead to oscillations in the loss function and prevent the model from converging to the best possible solution. In our analogy, taking large strides becomes counterproductive when you're trying to pinpoint the exact lowest point in a small valley; smaller, more careful steps are needed.

Illustration of loss curves with different fixed learning rates versus an ideal scenario where the rate decreases over time. A high rate causes oscillations, while a low rate converges slowly.

Conversely, if we start with a very small learning rate, training might be extremely slow. The optimizer takes tiny steps, requiring many iterations to reach a good minimum. Furthermore, a consistently small learning rate might increase the risk of getting trapped in suboptimal local minima or struggling to navigate saddle points effectively.

This presents a dilemma: the optimal learning rate seems to change during the training process. A high rate is good initially, while a lower rate is better later. This observation motivates the use of learning rate schedules.

A learning rate schedule is a strategy for adjusting the learning rate $\alpha$ dynamically during training, rather than keeping it fixed. The core idea is typically to start with a relatively high learning rate to benefit from rapid initial progress and then gradually decrease it as training proceeds. This reduction allows the optimizer to make finer adjustments, helping it converge more smoothly and accurately to a good minimum without excessive oscillation.

Employing a learning rate schedule can lead to several benefits:

• Potentially faster overall convergence compared to using a small, fixed learning rate from the start.
• Achieving a lower final training and validation loss by allowing the model to settle into a better minimum.
• Improved training stability, especially in the later stages.

While adaptive optimizers like Adam adjust learning rates on a per-parameter basis based on past gradients, learning rate schedules modify the global base learning rate over time (epochs or iterations). These two approaches are not mutually exclusive and can often be used together.

In the following sections, we will explore common strategies for implementing learning rate schedules, such as step decay, exponential decay, and cosine annealing, and discuss how to integrate them into your training workflow.