@Article{CiCP-31-4,
author = {Jingrun, Chen and Shi, Jin and Lyu, Liyao},
title = {A Consensus-Based Global Optimization Method with Adaptive Momentum Estimation},
journal = {Communications in Computational Physics},
year = {2022},
volume = {31},
number = {4},
pages = {1296--1316},
abstract = {<p style="text-align: justify;">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:<br/>• 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.<br/>• 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.<br/>• 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.</p>},
issn = {1991-7120},
doi = {https://doi.org/10.4208/cicp.OA-2021-0144},
url = {https://global-sci.com/article/79546/a-consensus-based-global-optimization-method-with-adaptive-momentum-estimation}
}