Analysis of a Natural Gradient Algorithm on Monotonic Convex-Quadratic-Composite Functions - Inria - Institut national de recherche en sciences et technologies du numérique Access content directly
Conference Papers Year : 2012

Analysis of a Natural Gradient Algorithm on Monotonic Convex-Quadratic-Composite Functions

Youhei Akimoto
  • Function : Author
  • PersonId : 924013

Abstract

In this paper we investigate the convergence properties of a variant of the Covariance Matrix Adaptation Evolution Strategy (CMA-ES). Our study is based on the recent theoretical foundation that the pure rank-mu update CMA-ES performs the natural gradient descent on the parameter space of Gaussian distributions. We derive a novel variant of the natural gradient method where the parameters of the Gaussian distribution are updated along the natural gradient to improve a newly defined function on the parameter space. We study this algorithm on composites of a monotone function with a convex quadratic function. We prove that our algorithm adapts the covariance matrix so that it becomes proportional to the inverse of the Hessian of the original objective function. We also show the speed of covariance matrix adaptation and the speed of convergence of the parameters. We introduce a stochastic algorithm that approximates the natural gradient with finite samples and present some simulated results to evaluate how precisely the stochastic algorithm approximates the deterministic, ideal one under finite samples and to see how similarly our algorithm and the CMA-ES perform.
Fichier principal
Vignette du fichier
pap157s1-akimoto.pdf (504.69 Ko) Télécharger le fichier
Origin : Files produced by the author(s)
Loading...

Dates and versions

hal-00688909 , version 1 (18-04-2012)

Identifiers

Cite

Youhei Akimoto. Analysis of a Natural Gradient Algorithm on Monotonic Convex-Quadratic-Composite Functions. Genetic and Evolutionary Computation Conference (GECCO 2012), Jul 2012, Philadelphia, United States. ⟨hal-00688909⟩
454 View
347 Download

Altmetric

Share

Gmail Facebook X LinkedIn More