CMA-ES for Safe Optimization
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arXiv
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| Main Authors: | , , , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866911879256866816 |
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| author | Uchida, Kento Hamano, Ryoki Nomura, Masahiro Saito, Shota Shirakawa, Shinichi |
| author_facet | Uchida, Kento Hamano, Ryoki Nomura, Masahiro Saito, Shota Shirakawa, Shinichi |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_10534 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | CMA-ES for Safe Optimization Uchida, Kento Hamano, Ryoki Nomura, Masahiro Saito, Shota Shirakawa, Shinichi Neural and Evolutionary Computing 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. |
| title | CMA-ES for Safe Optimization |
| topic | Neural and Evolutionary Computing |
| url | https://arxiv.org/abs/2405.10534 |