what is meaninig of “until convergence” in gradient decent
Machine learning
why you have taken iteration equal to 100 only we have to iterate till "the gradient equal =0’ na
Until convergence means till the point where your loss or error is not reducing anymore. The local minima or global minima point.
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This implies that in order to achieve a bound of f(x(k))−f(x∗) ≤ ϵ, we must run O(1/ϵ) iterations of gradient descent. This rate is referred to as “sub-linear convergence.” Strongly convex f. In contrast, if we assume that f is strongly convex, we can show that gradient descent converges with rate O(ck) for 0 <c< 1. Radient Descent is an optimization algorithm for finding a local minimum of a differentiable function. Gradient descent is simply used to find the values of a function’s parameters (coefficients) that minimize a cost function as far as possible.
The Gradient descent algorithm multiplies the gradient by a number (Learning rate or Step size) to determine the next point. For example: having a gradient with a magnitude of 4.2 and a learning rate of 0.01, then the gradient descent algorithm will pick the next point 0.042 away from the previous point.
This implies that so as to realize abound of f(x(k))−f(x∗) ≤ ϵ, we must run O(1/ϵ) iterations of gradient descent. This rate is mentioned as “sub-linear convergence.” Strongly convex f. In contrast, if we assume that f is strongly convex, we will show that gradient descent converges with rate O(ck) for 0.
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