![]() ![]() Gradient descent with the exact step length only took us two iterations until it found the minimum. Ggtitle(bquote(atop("Gradient Descent for" ~ x^2, "With Exact Step Length and k = 2"))) Plot.title = element_text(hjust = 0.5, size = 18) Geom_point(data = data_points, aes(x = x, y = y), col = "red") + Geom_line(data = data_points, aes(x = x, y = y), col = "blue") + The framework for the gradient descent algorithm looks like this:Īlpha=0.05 (alpha denotes our step length) Let’s consider one simple example where we try to find the value x for which x^2 is minimized. The step length (how far in that direction should we go?).The objective function (also sometimes called cost function).Now, the four most important things we need to know for gradient descent are: After that, we walk in that direction by deciding on an appropriate step length. We do that by taking the derivative of the objective function, then decide on a descent direction that yields the steepest decrease in the function value. To get an intuition about gradient descent, we are minimizing x^2 by finding a value x for which the function value is minimal. It is a popular technique in machine learning and neural networks. The gradient descent method is an iterative optimization method that tries to minimize the value of an objective function. Does gradient descent always find the minimum of a function?.Backtracking line search (line search method).Inexact line search methods and Wolfe conditions (line search method).Gradient descent and line search methods.The gradient descent algorithm with constant step length.What we are going to cover in this post is: In this blog post, we are going over the gradient descent algorithm and some line search methods to minimize the objective function x^2. This algorithm can be used in machine learning for example to find the optimal beta coefficients that are minimizing the objective function of a linear regression. The gradient descent algorithm is an optimization technique that can be used to minimize objective function values. ![]()
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