Learning Rate – 1-Cycle Scheduling, exponential decay and Cyclic Exponential Decay (CED) – Part 4 – Day 45

Advanced Learning Rate Scheduling Methods for Machine Learning: Learning rate scheduling is critical in optimizing machine learning models, helping them converge faster and avoid pitfalls such as getting stuck in local minima. So far in our pervious days articles we have explained a lot about optimizers, learning rate schedules, etc. In this guide, we explore three key learning rate schedules: Exponential Decay, Cyclic Exponential Decay (CED), and 1-Cycle Scheduling, providing mathematical proofs, code implementations, and theory behind each method. 1. Exponential Decay Learning Rate Exponential Decay reduces the learning rate by a factor of , allowing larger updates early in training and smaller, more refined updates as the model approaches convergence. Formula: Where: is the learning rate at time step , is the initial learning rate, is the decay rate, controlling how fast the learning rate decreases, represents the current time step (or epoch). Mathematical Proof of Exponential Decay The core idea of exponential decay is that the learning rate decreases over time. Let’s prove that this results in convergence. The parameter update rule for gradient descent is: Substituting the exponentially decayed learning rate: As , the decay factor , meaning that the updates to become smaller and smaller, allowing…