TY - GEN

T1 - Exponential natural evolution strategies

AU - Glasmachers, Tobias

AU - Schaul, Tom

AU - Yi, Sun

AU - Wierstra, Daan

AU - Schmidhuber, Jürgen

N1 - Generated from Scopus record by KAUST IRTS on 2022-09-14

PY - 2010/8/27

Y1 - 2010/8/27

N2 - The family of natural evolution strategies (NES) offers a principled approach to real-valued evolutionary optimization by following the natural gradient of the expected fitness. Like the well-known CMA-ES, the most competitive algorithm in the field, NES comes with important invariance properties. In this paper, we introduce a number of elegant and efficient improvements of the basic NES algorithm. First, we propose to parameterize the positive definite covariance matrix using the exponential map, which allows the covariance matrix to be updated in a vector space. This new technique makes the algorithm completely invariant under linear transformations of the underlying search space, which was previously achieved only in the limit of small step sizes. Second, we compute all updates in the natural coordinate system, such that the natural gradient coincides with the vanilla gradient. This way we avoid the computation of the inverse Fisher information matrix, which is the main computational bottleneck of the original NES algorithm. Our new algorithm, exponential NES (xNES), is significantly simpler than its predecessors. We show that the various update rules in CMA-ES are closely related to the natural gradient updates of xNES. However, xNES is more principled than CMA-ES, as all the update rules needed for covariance matrix adaptation are derived from a single principle. We empirically assess the performance of the new algorithm on standard benchmark functions. Copyright 2010 ACM.

AB - The family of natural evolution strategies (NES) offers a principled approach to real-valued evolutionary optimization by following the natural gradient of the expected fitness. Like the well-known CMA-ES, the most competitive algorithm in the field, NES comes with important invariance properties. In this paper, we introduce a number of elegant and efficient improvements of the basic NES algorithm. First, we propose to parameterize the positive definite covariance matrix using the exponential map, which allows the covariance matrix to be updated in a vector space. This new technique makes the algorithm completely invariant under linear transformations of the underlying search space, which was previously achieved only in the limit of small step sizes. Second, we compute all updates in the natural coordinate system, such that the natural gradient coincides with the vanilla gradient. This way we avoid the computation of the inverse Fisher information matrix, which is the main computational bottleneck of the original NES algorithm. Our new algorithm, exponential NES (xNES), is significantly simpler than its predecessors. We show that the various update rules in CMA-ES are closely related to the natural gradient updates of xNES. However, xNES is more principled than CMA-ES, as all the update rules needed for covariance matrix adaptation are derived from a single principle. We empirically assess the performance of the new algorithm on standard benchmark functions. Copyright 2010 ACM.

UR - http://portal.acm.org/citation.cfm?doid=1830483.1830557

UR - http://www.scopus.com/inward/record.url?scp=77955901414&partnerID=8YFLogxK

U2 - 10.1145/1830483.1830557

DO - 10.1145/1830483.1830557

M3 - Conference contribution

SN - 9781450300728

SP - 393

EP - 400

BT - Proceedings of the 12th Annual Genetic and Evolutionary Computation Conference, GECCO '10

ER -