Combining Gaussian processes and neural networks in surrogate modeling for covariance matrix adaptation evolution strategy
Abstract
This paper focuses on surrogate models for Covariance Matrix Adaptation Evolution Strategy (CMA-ES) in continuous black-box optimization. Surrogate modeling has proven to be able to decrease the number of evaluations of the objective function, which is an important requirement in some real-world applications where the evaluation can be costly or time-demanding.
Surrogate models achieve this by providing an approximation instead of the evaluation of the true objective function. One of the state-of-the-art models for this task is the Gaussian process.
We present an approach to combining Gaussian processes with artificial neural networks, which was previously successfully applied to other machine learning domains. The experimental part employs data recorded from previous CMA-ES runs, allowing us to assess different settings of surrogate models without running the whole CMA-ES algorithm.
The data were collected using 24 noiseless benchmark functions of the platform for comparing continuous optimizers COCO in 5 different dimensions. Overall, we used data samples from over 2.8 million generations of CMA-ES runs.
The results examine and statistically compare six covariance functions of Gaussian processes with the neural network extension. So far, the combined model did not show up to outperform the Gaussian process alone.
Therefore, in conclusion, we discuss possible reasons for this and ideas for future research.