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Gradient descent is an optimization algorithm used to minimize the error or cost function in machine learning models. It is commonly used in training models such as linear regression and neural networks. The basic idea behind gradient descent is to iteratively update the model parameters, such as weights and biases, in the direction of steepest descent of the cost function. This is done by calculating the gradient of the cost function with respect to the parameters and taking steps proportional to the negative of the gradient. The algorithm starts with some initial values for the parameters and updates them using the following update rule: θ_new = θ_old - learning_rate * ∇J(θ_old) where: - θ_new are the new values of the parameters - θ_old are the old values of the parameters - learning_rate is a hyperparameter that controls the size of the steps taken in each iteration - ∇J is the gradient of the cost function J with respect to the parameters The process is repeated until a specified termination condition is met, such as reaching a maximum number of iterations or when the change in the cost function is below a certain threshold. By iteratively adjusting the parameters in the direction of decreasing error, gradient descent allows the model to converge to a locally optimal solution. However, it should be noted that gradient descent is not guaranteed to find the global optimum, especially in non-convex cost functions. There are different variants of gradient descent, such as batch gradient descent, stochastic gradient descent, and mini-batch gradient descent, which differ in the amount of data used to compute the gradient and update the parameters in each iteration. These variants have different trade-offs in terms of convergence speed and computational efficiency.

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