Q2.16 Assume a differentiable objective function f x is Lipschitz continuous; namely, there exists a real constant
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Q2.16 Assume a differentiable objective function f ¹xº is Lipschitz continuous; namely, there exists a real constant L > 0, and for any two points x1 and x2, f ¹x1º ???? f ¹x2º
L kx1 ???? x2 k always holds. Prove that the gradient descent Algorithm 2.1 always converges to a stationary point, namely, limn!1 kr f ¹x¹nººk = 0, as long as all used step sizes are small enough, satisfying n < 1L.
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Machine Learning Fundamentals A Concise Introduction
ISBN: 9781108940023
1st Edition
Authors: Hui Jiang
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