# CMA-ES for Safe Optimization

arXiv: https://arxiv.org/abs/2405.10534 · HTML: https://mlsanity.com/paper/2405.10534/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 17 May 2024.

## Built on by (most cited first, 2 of 2)

- [REALM: A Real-to-Sim Validated Benchmark for Generalization in Robotic Manipulation](https://mlsanity.com/paper/2512.19562/) (2025)
- [Harnessing Bounded-Support Evolution Strategies for Policy Refinement](https://mlsanity.com/paper/2511.09923/) (2025)

## Abstract (arXiv)

In several real-world applications in medical and control engineering, there are unsafe solutions whose evaluations involve inherent risk. This optimization setting is known as safe optimization and formulated as a specialized type of constrained optimization problem with constraints for safety functions. Safe optimization requires performing efficient optimization without evaluating unsafe solutions. A few studies have proposed the optimization methods for safe optimization based on Bayesian optimization and the evolutionary algorithm. However, Bayesian optimization-based methods often struggle to achieve superior solutions, and the evolutionary algorithm-based method fails to effectively reduce unsafe evaluations. This study focuses on CMA-ES as an efficient evolutionary algorithm and proposes an optimization method termed safe CMA-ES. The safe CMA-ES is designed to achieve both safety and efficiency in safe optimization. The safe CMA-ES estimates the Lipschitz constants of safety functions transformed with the distribution parameters using the maximum norm of the gradient in Gaussian process regression. Subsequently, the safe CMA-ES projects the samples to the nearest point in the safe region constructed with the estimated Lipschitz constants. The numerical simulation using the benchmark functions shows that the safe CMA-ES successfully performs optimization, suppressing the unsafe evaluations, while the existing methods struggle to significantly reduce the unsafe evaluations.