A Comprehensive Guide to AdaGrad: Origins, Mechanism, and Mathematical Proof – Day 37

  A Comprehensive Guide to AdaGrad: Origins, Mechanism, and Mathematical Proof Introduction to AdaGrad AdaGrad, short for Adaptive Gradient Algorithm, is a foundational optimization algorithm in machine learning and deep learning. It was introduced in 2011 by John Duchi, Elad Hazan, and Yoram Singer in their paper titled “Adaptive Subgradient Methods for Online Learning and Stochastic Optimization”. AdaGrad revolutionized the field by offering a solution to the limitations of traditional gradient descent, especially in scenarios involving sparse data and high-dimensional optimization problems. The Origins of AdaGrad The motivation behind AdaGrad was to improve the robustness and efficiency of the Stochastic Gradient Descent (SGD) method. In high-dimensional spaces, using a fixed learning rate for all parameters can be inefficient. Some parameters might require a larger step size while others may need smaller adjustments. AdaGrad addresses this by adapting the learning rate individually for each parameter, which allows for better handling of the varying scales in the data. How AdaGrad Works The core idea of AdaGrad is to accumulate the squared gradients for each parameter over time and use this information to scale the learning rate. This means that parameters with large accumulated gradients receive smaller updates, while those with smaller gradients…