Gaussian Process Surrogate Models for the CMA Evolution Strategy.

Area of Science:

• Optimization algorithms
• Machine learning applications
• Evolutionary computation

Background:

• Covariance Matrix Adaptation Evolutionary Strategy (CMA-ES) is a powerful optimization algorithm.
• Surrogate models can accelerate optimization by approximating objective functions.
• Gaussian processes are effective probabilistic surrogate models.

Purpose of the Study:

• To present and evaluate Gaussian process surrogate models for CMA-ES.
• To investigate the benefits of Gaussian process uncertainty prediction in surrogate-assisted optimization.
• To compare novel DTS-CMA-ES algorithm against state-of-the-art optimizers.

Main Methods:

• Implementation and evaluation of five Gaussian process surrogate models for CMA-ES.
• Development and detailed analysis of the DTS-CMA-ES algorithm.
• Benchmarking against six other state-of-the-art black-box optimizers on COCO benchmarks.

Main Results:

• The DTS-CMA-ES algorithm demonstrates comparable or faster convergence than existing optimizers.
• Performance gains are observed for limited function evaluation budgets (25-100 evaluations/dimension).
• Significant advantages are noted in 10-dimensional or less spaces (25-250 evaluations/dimension).

Conclusions:

• Gaussian process surrogate models offer significant benefits for CMA-ES, especially with uncertainty prediction.
• DTS-CMA-ES is a highly effective algorithm for low-dimensional black-box optimization with limited budgets.
• The proposed approach advances the field of surrogate-assisted evolutionary optimization.