The AdaGrad algorithm, short for Adaptive Gradient Algorithm, is an optimization technique designed to improve the performance of gradient descent. It adapts the learning rate for each parameter based on the historical gradients, allowing for more effective optimization, especially in scenarios where the curvature of the objective function varies across dimensions.

In AdaGrad, an initial step size is set for all input variables, typically around 0.01. The algorithm maintains an internal variable for each input that accumulates the squared gradients observed during the optimization process. The custom step size for each parameter is calculated by dividing the initial step size by the square root of this accumulated sum, which helps to adjust the learning rate dynamically. This means that parameters with larger gradients will have smaller updates, while those with smaller gradients will have larger updates, effectively allowing the algorithm to navigate the search space more efficiently ¹².

One of the advantages of AdaGrad is its reduced sensitivity to the initial learning rate compared to standard gradient descent, making it a popular choice for various machine learning tasks.