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A consensus-based Global optimization Method with Adaptive Momentum Estimation

Communications in Computational Physics 2022年第4期31卷 1296-1316页

作者： Jingrun Chen Shi Jin Liyao Lyu School of Mathematical Sciences University of Science and Technology of ChinaHefeiAnhui 230026China Suzhou Institute for Advanced Research University of Science and Technology of ChinaSuzhouJiangsu 215123China School of Mathematical Sciences Institute of Natural SciencesMOE-LSCShanghai Jiao Tong UniversityShanghai200240China Department of Computational Mathematics Scienceand EngineeringMichigan State UniversityEast LansingMI48824USA

Objective functions in large-scalemachine-learning and artificial intelligence applications often live in high dimensions with strong non-convexity and massive local ***-based methods,such as the stochastic gradient method and Adam[15],and gradient-freemethods,such as the consensus-based optimization(CBO)method,can be employed to find *** 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 *** 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 *** can handle non-differentiable activation functions and thus approximate lowregularity functions with better *** 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 *** is robust in the sense that its convergence is insensitive to the learning rate by a linear stability *** is confirmed by finding theminimizer of a quadratic function.

关键词： consensus-based optimization global optimization machine learning curse of dimensionality

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