Lecture Note
University
Stanford UniversityCourse
CS229 | Machine LearningPages
2
Academic year
2023
anon
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45
Understanding the Algorithm for Gradient Descent: A DeepDive Many machine learning methods depend on gradient descent, thus understanding what itdoes and how it operates is critical for anyone who wishes to have a solid grasp of thesealgorithms. We will go deeply into gradient descent in this post, learning more about its innerworkings and developing a clearer understanding of what it is doing and why it makes sense. The Gradient Descent Algorithm: An Overview The gradient descent algorithm's fundamental purpose is to minimize a cost function bychanging model parameters. The cost function, J, is a function of the model's twoparameters, w and b, in the most basic form of gradient descent. In order to minimize thecost J, the gradient descent algorithm updates the parameters w and b. The size of the step that is performed when updating the parameters is determined by thelearning rate, which is represented by the Greek letter alpha. The cost function J's slope atthe current values of the parameters is measured by the derivative term, d over dw. Bydeducting the learning rate times the derivative of J from the parameter values as theycurrently stand, the gradient descent algorithm updates the parameters. Reducing the Issue to One Parameter We may make the problem simpler by considering the scenario in which there is only oneparameter, w, in order to acquire a clearer understanding of what the learning rate andderivative term are doing in gradient descent. The gradient descent algorithm then becomes: 𝑤 = 𝑤 − α · ( 𝑑 𝑑𝑤 ) 𝐽(𝑤) By altering the parameter w, the objective in this example is to minimize the cost function Jof w. In order to do this, gradient descent is started at a certain initial value of w, and w isupdated using the formula above. The Derivative's Function It is useful to think of the derivative as the slope of the cost function J at a specific position inorder to comprehend what the derivative term is doing in gradient descent. At this location, atangent line that touches the cost function J's curve can be created. This line's slope, whichat that time represents the derivative of J, tells us something about how the cost function isevolving. The slope and derivative are both positive if the tangent line is pointed up and to the right.The updated value of w in this situation will be w minus alpha times a positive number, whichwill result in a lower value of w. By decreasing the cost J and bringing the method closer tothe minimum of J, gradient descent is going to the left on the J curve. Gradient Descent is used In machine learning, gradient descent is a potent method that may be used to reduce avariety of cost functions. Gradient descent can, however, become stuck in local minima orconverge too slowly, thus it must be used carefully. There are numerous methods for dealing
with these problems, such as applying adaptive learning rates, selecting various optimizationalgorithms, or changing the cost function to make optimization easier. Gradient descent is a powerful and adaptable optimization method that is frequentlyemployed in a range of machine learning applications. When you have a better knowledge ofwhat gradient descent does and why it makes sense, you can utilize it to your advantage inmachine learning projects to get fantastic outcomes.
The Algorithm for Gradient Descent
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