Abstract
The information geometric optimization (IGO) flow has been introduced recently by Arnold et al. This distinguished mathematical flow on the parameter manifold of a family of search distributions constitutes a novel approach to the analysis of several randomized search heuristics, including modern evolution strategies. Besides its appealing theoretical properties, it offers the unique opportunity to approach the convergence analysis of evolution strategies in two independent steps. The first step is the analysis of the flow itself, or more precisely, the convergence of its trajectories to Dirac peaks over the optimum. In a second step it remains to study the deviation of actual algorithm trajectories from the continuous flow. The present study approaches the first problem. The IGO flow of isotropic Gaussian search distributions is analyzed on convex, quadratic fitness functions. Convergence of all trajectories to the Dirac peak over the optimum is established.
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Glasmachers, T. (2012). Convergence of the IGO-Flow of Isotropic Gaussian Distributions on Convex Quadratic Problems. In: Coello, C.A.C., Cutello, V., Deb, K., Forrest, S., Nicosia, G., Pavone, M. (eds) Parallel Problem Solving from Nature - PPSN XII. PPSN 2012. Lecture Notes in Computer Science, vol 7491. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-32937-1_1
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DOI: https://doi.org/10.1007/978-3-642-32937-1_1
Publisher Name: Springer, Berlin, Heidelberg
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