Comparing natural evolution strategies to BIPOP-CMA-ES on noiseless and noisy black-box optimization testbeds

Tom Schaul
2012 Proceedings of the fourteenth international conference on Genetic and evolutionary computation conference companion - GECCO Companion '12  
Natural Evolution Strategies (NES) are a recent member of the class of real-valued optimization algorithms that are based on adapting search distributions. Exponential NES (xNES) are the most common instantiation of NES, and particularly appropriate for the BBOB 2012 benchmarks, given that many are non-separable, and their relatively small problem dimensions. Here, we augment xNES with adaptation sampling, which adapts learning rates online, and compare the resulting performance directly to the
more » ... nce directly to the BIPOP-CMA-ES algorithm, the winner of the 2009 black-box optimization benchmarking competition (BBOB). This report provides an extensive empirical comparison, both on the noise-free and noisy BBOB testbeds. Natural evolution strategies (NES) maintain a search distribution π and adapt the distribution parameters θ by following the natural gradient [1] of expected fitness J, that is, maximizing Just like their close relative CMA-ES [12], NES algorithms are invariant under monotone transformations of the fitness function and linear transformations of the search space. Each iteration the algorithm produces n samples zi ∼ π(z|θ), i ∈ {1, . . . , n}, i.i.d. from its search distribution, which is parameterized by θ. The gradient w.r.t. the parameters θ can
doi:10.1145/2330784.2330819 dblp:conf/gecco/Schaul12e fatcat:3spg5gkiwjgdzjonzn6pzttvhq