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Anderson Acceleration of Gradient Methods with Energy for Optimization Problems
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Anderson acceleration(AA)is an extrapolation technique designed to speed up fixed-point iterations.For optimization problems,we propose a novel algorithm by combining the AA with the energy adaptive gradient method(AEGD)[arXiv:2010.05109].The feasibility of our algorithm is ensured in light of the convergence theory for AEGD,though it is not a fixed-point iteration.We provide rigorous convergence rates of AA for gradient descent(GD)by an acceleration factor of the gain at each implementation of AA-GD.Our experi-mental results show that the proposed AA-AEGD algorithm requires little tuning of hyper-parameters and exhibits superior fast convergence.
Anderson acceleration(AA)Gradient descent(GD)Energy stability
Hailiang Liu、Jia-Hao He、Xuping Tian
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Department of Mathematics,Iowa State University,Ames,IA,USA
Department of Agricultural and Biosystems Engineering,Iowa State University,Ames,IA,USA
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