In Gradient Descent, refers to the magnitude of updates to the parameters, and refers to the direction of updates.
Question
In Gradient Descent, refers to the magnitude of updates to the parameters, and refers to the direction of updates.
Solution
In Gradient Descent, the learning rate refers to the magnitude of updates to the parameters, and the gradient refers to the direction of updates.
Here's a step-by-step explanation:
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Gradient Descent is an optimization algorithm used to minimize some function by iteratively moving in the direction of steepest descent as defined by the negative of the gradient.
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The learning rate, often denoted by alpha, determines the size of the steps we take to reach a (local) minimum. In other words, it determines how quickly or slowly we move towards the optimal weights.
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The gradient, on the other hand, gives the direction of the steepest ascent. The negative of the gradient gives the direction of steepest descent. This is the direction we want to move in since we are trying to minimize a function.
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In each iteration of the gradient descent, we update the parameters (weights) by subtracting the product of learning rate and the gradient from the current parameters. This means we move a step (determined by the learning rate) in the direction of the steepest descent (determined by the gradient).
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This process is repeated until the algorithm converges to an optimal solution, i.e., until the change in parameters becomes very small or the maximum number of iterations is reached.
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