Year: 2022
Author: Jingrun Chen, Shi Jin, Liyao Lyu
Communications in Computational Physics, Vol. 31 (2022), Iss. 4 : pp. 1296–1316
Abstract
Objective functions in large-scale machine-learning and artificial intelligence
applications often live in high dimensions with strong non-convexity and massive
local minima. Gradient-based methods, such as the stochastic gradient method and
Adam [15], and gradient-free methods, such as the consensus-based optimization (CBO)
method, can be employed to find minima. In this work, based on the CBO method and
Adam, we propose a consensus-based global optimization method with adaptive momentum estimation (Adam-CBO). Advantages of the Adam-CBO method include:
• It is capable of finding global minima of non-convex objective functions with
high success rates and low costs. This is verified by finding the global minimizer
of the 1000 dimensional Rastrigin function with 100% success rate at a cost only
growing linearly with respect to the dimensionality.
• It can handle non-differentiable activation functions and thus approximate low-regularity functions with better accuracy. This is confirmed by solving a machine learning task for partial differential equations with low-regularity solutions
where the Adam-CBO method provides better results than Adam.
• It is robust in the sense that its convergence is insensitive to the learning rate by a
linear stability analysis. This is confirmed by finding the minimizer of a quadratic
function.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/cicp.OA-2021-0144
Communications in Computational Physics, Vol. 31 (2022), Iss. 4 : pp. 1296–1316
Published online: 2022-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 21
Keywords: Consensus-based optimization global optimization machine learning curse of dimensionality.