Natural gradient works efficiently in learning
Neural Computation
Convergence results for the (1, λ)-SA-ES using the theory of ϕ-irreducible Markov chains
Theoretical Computer Science
Completely Derandomized Self-Adaptation in Evolution Strategies
Evolutionary Computation
Exponential natural evolution strategies
Proceedings of the 12th annual conference on Genetic and evolutionary computation
High dimensions and heavy tails for natural evolution strategies
Proceedings of the 13th annual conference on Genetic and evolutionary computation
General lower bounds for evolutionary algorithms
PPSN'06 Proceedings of the 9th international conference on Parallel Problem Solving from Nature
Theoretical Computer Science
Proceedings of the 14th annual conference companion on Genetic and evolutionary computation
Proceedings of the 14th annual conference companion on Genetic and evolutionary computation
Proceedings of the 14th annual conference companion on Genetic and evolutionary computation
Proceedings of the 14th annual conference companion on Genetic and evolutionary computation
Proceedings of the 14th annual conference companion on Genetic and evolutionary computation
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This theoretical investigation gives the first proof of convergence for (radial) natural evolution strategies, on d-dimensional sphere functions, and establishes the conditions on hyper-parameters, as a function of d. For the limit case of large population sizes we show asymptotic linear convergence, and in the limit of small learning rates we give a full analytic characterization of the algorithm dynamics, decomposed into transient and asymptotic phases. Finally, we show why omitting the natural gradient is catastrophic.