Intensive surrogate model exploitation in self-adaptive surrogate-assisted cma-es (saacm-es)

Abstract

This paper presents a new mechanism for a better exploitation of surrogate models in the framework of Evolution Strategies (ESs). This mechanism is instantiated here on the self-adaptive surrogate-assisted Covariance Matrix Adaptation Evolution Strategy ( s * ACM-ES), a recently proposed surrogate-assisted variant of CMA-ES. As well as in the original s * ACM-ES, the expensive function is optimized by exploiting the surrogate model, whose hyper-parameters are also optimized online. The main novelty concerns a more intensive exploitation of the surrogate model by using much larger population sizes for its optimization.The new variant of s * ACM-ES significantly improves the original s *ACM-ES and further increases the speed-up compared to the CMA-ES, especially on unimodal functions (e.g., on 20-dimensional Rotated Ellipsoid, s * ACM-ES is 6 times faster than aCMA-ES and almost by one order of magnitude faster than CMA-ES). The empirical validation on the BBOB-2013 noiseless testbed demonstrates the efficiency and the robustness of the proposed mechanism.

Model-Based Relative Entropy Stochastic Search

“…Surrogate based stochastic search algorithms [6] [13] have been shown to be more sample efficient than direct stochastic search methods and can also smooth out the noise of the objective function. For example, an individual optimization method is used on the surrogate that is stopped whenever the KL-divergence between the new and the old distribution exceeds a certain bound [6].…”

“…For example, an individual optimization method is used on the surrogate that is stopped whenever the KL-divergence between the new and the old distribution exceeds a certain bound [6]. For the first time, our algorithm uses the surrogate model to compute the new search distribution analytically, which bounds the KL divergence of the new and old search distribution, in closed form.…”

“…We compared our algorithm against CMA-ES, NES, PoWER and REPS. In each iteration, we generated 15 new samples 6 . For MORE, REPS and PoWER, we always keep the last L = 150 samples, while for NES and CMA-ES only the 15 current samples are kept 7 .…”

Bi-population CMA-ES agorithms with surrogate models and line searches

“…An extension of s * ACM-ES, based on this idea, referred to as s * ACM-ES-k, has been proposed in [18]. In s * ACM-ES-k,f is optimized forn generations by CMA-ES with population size λ = k λ λ def ault and number of parents µ = kµµ def ault , where k λ ≥ 1 and kµ ≥ 1.…”

“…For benchmarking we consider five CMA-ES algorithms in BIPOP restart scenario [3]: BIPOP-aCMA-ES [16,3], BIPOP-s * aACM-ES [17], BIPOP-s * aACM-ES-k [18], BIPOPaCMA-STEP and HCMA 1 . For all but BIPOP-s * aACM-ESk [18] and BIPOP-aCMA-STEP algorithms the BBOB results are taken from the literature.…”