Exponential natural evolution strategies

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 computa...

• Type: Conference
• Year: 2010
• Where: GECCO
• Authors: Tobias Glasmachers, Tom Schaul, Yi Sun, Daan Wierstra, Jürgen Schmidhuber
• Keywords: Covariance Matrix, Evolution Strategies, GECCO 2010, Natural Gradient, Optimization