Answered: Gradient descent is a widely used…

Database System Concepts

7th Edition

ISBN:9780078022159

Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Chapter1: Introduction

Section: Chapter Questions

Problem 1PE

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Gradient descent is a widely used optimization algorithm in machine learning and deep learning. It is used to find the minimum value of a differentiable function by iteratively adjusting the parameters of the function in the direction of the steepest decrease of the function's value. In gradient descent, the function is first differentiated to find its gradient, which is a vector of the partial derivatives with respect to each of the parameters. The gradient points in the direction of the steepest increase of the function, so to find the minimum, we need to move in the opposite direction, i.e., in the direction of the negative gradient. The algorithm starts from an initial guess for the parameters and iteratively adjusts the parameters by subtracting a small fraction of the gradient from the current parameters. The fraction is determined by the learning rate, which is a hyperparameter that controls the step size of the update. The algorithm updates the parameters until either a maximum number of iterations is reached or the change in the parameters is smaller than a specified tolerance. Gradient descent is a simple and effective optimization algorithm for many functions, but it has some limitations. For example, it can get stuck in local minima, which are minima that are not the global minimum of the function. To overcome these limitations, there are variants of gradient descent, such as mini-batch gradient descent and stochastic gradient descent, which randomly sample the data to update the parameters, and momentum gradient descent, which adds a term to the update to increase the stability of the optimization. Psuedocode Input: initial guess x, learning rate a, maximum number of iterations N Output: minimum of the function f 1. Set iteration counter i = 0 2. Repeat the following until convergence or i = N a. Compute the gradient of f at x, denoted by grad_f(x) b. Update x: x = x - a * grad_f(x) c. Increment iteration counter i = i + 1 3. Return x as the minimum of How to prepare report Students should prepare their own reports. No collaboration is allowed, and the cheating policy discussed in first lecture will be applied. In general, honor code rules will be followed. • Design Code: Basically, you need to put your C/C++ code for this project. You are allowed to develop code in C or C++. • Your comments: Just source code won’t be accepted. You need to explain how your code works and put enough explanation for your design. • Your report must be prepared in english. Report in different language won't be evaluated. • Screenshots for all cases must be provided.

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