Not recommended for large training samples.

Example of descent direction. Faster and uses less resources than Batch Gradient descent. The central investigation of this paper is the computation of the line search for a given set of descent directions. The function value at the starting point is.

The gradient of this function is rf f x. Uses the whole training sample. The reader will recall that is a descent direction for f at xk if.

Method of Steepest Descent The main idea of t h e descent method is that we start with a starting point of x try to find the next point thats closer to the solution iterate over the process until we find the final solution. You may have learned in calculus that the gradient is the direction of steepest ascent While this is true it is only true under the assumption that mathcalX is a Euclidean space ie a space where it makes sense to measure the distance between two points with the Euclidean distance. For example at step k we are at the point 𝑥 𝑘.

F y 2x p 16 24x y2. Stochastic Gradient Descent is a stochastic as in probabilistic spin on Gradient Descent. Diagonally Scaled Steepest Descent.

We rst compute the steepest descent direction from rfxy 8x 4y4y 4x to obtain rfx 0 rf23 44. Gradient Descent is one of the most popular methods to pick the model that best fits the training data. Stochastic Gradient descent Batch Gradient descent.

The direction of steepest descent for x f x at any point is dc or dc 2 Example. 1 2 3 without being exhaustive propose different formulas for the line search. More expensive but can have much faster convergence.