Accelerated Optimization for Machine Learning by Zhouchen Lin & Huan Li & Cong Fang

Author:Zhouchen Lin & Huan Li & Cong Fang
Language: eng
Format: epub
ISBN: 9789811529108
Publisher: Springer Singapore

Moreover, with the KŁ property we can give the convergence rate of Algorithm 4.1. As a comparison, the convergence rate of gradient descent for the general nonconvex problem is in the form of min0≤k≤K∥dist(0, ∂F(x k))∥2 ≤ O(1∕K) [23].

Theorem 4.3

Assume that 1)–3) of Assumption 4.1 hold and the desingularizing function φ has the form of for some C > 0, θ ∈ (0, 1]. Let F ∗ = F(x) for all x ∈  Ω and r k = F(x k) − F ∗, then with the sequence {x k} generated by Algorithm 4.1 satisfies 1.If θ = 1, then there exists k 1 such that F(x k) = F ∗ for all k > k 1 and the algorithm terminates in finite steps;

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