CMA-ES with Learning Rate Adaptation
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866909327440216064 |
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| author | Nomura, Masahiro Akimoto, Youhei Ono, Isao |
| author_facet | Nomura, Masahiro Akimoto, Youhei Ono, Isao |
| contents | The covariance matrix adaptation evolution strategy (CMA-ES) is one of the most successful methods for solving continuous black-box optimization problems. A practically useful aspect of the CMA-ES is that it can be used without hyperparameter tuning. However, the hyperparameter settings still have a considerable impact on performance, especially for difficult tasks, such as solving multimodal or noisy problems. This study comprehensively explores the impact of learning rate on the CMA-ES performance and demonstrates the necessity of a small learning rate by considering ordinary differential equations. Thereafter, it discusses the setting of an ideal learning rate. Based on these discussions, we develop a novel learning rate adaptation mechanism for the CMA-ES that maintains a constant signal-to-noise ratio. Additionally, we investigate the behavior of the CMA-ES with the proposed learning rate adaptation mechanism through numerical experiments, and compare the results with those obtained for the CMA-ES with a fixed learning rate and with population size adaptation. The results show that the CMA-ES with the proposed learning rate adaptation works well for multimodal and/or noisy problems without extremely expensive learning rate tuning. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_15876 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | CMA-ES with Learning Rate Adaptation Nomura, Masahiro Akimoto, Youhei Ono, Isao Neural and Evolutionary Computing Optimization and Control The covariance matrix adaptation evolution strategy (CMA-ES) is one of the most successful methods for solving continuous black-box optimization problems. A practically useful aspect of the CMA-ES is that it can be used without hyperparameter tuning. However, the hyperparameter settings still have a considerable impact on performance, especially for difficult tasks, such as solving multimodal or noisy problems. This study comprehensively explores the impact of learning rate on the CMA-ES performance and demonstrates the necessity of a small learning rate by considering ordinary differential equations. Thereafter, it discusses the setting of an ideal learning rate. Based on these discussions, we develop a novel learning rate adaptation mechanism for the CMA-ES that maintains a constant signal-to-noise ratio. Additionally, we investigate the behavior of the CMA-ES with the proposed learning rate adaptation mechanism through numerical experiments, and compare the results with those obtained for the CMA-ES with a fixed learning rate and with population size adaptation. The results show that the CMA-ES with the proposed learning rate adaptation works well for multimodal and/or noisy problems without extremely expensive learning rate tuning. |
| title | CMA-ES with Learning Rate Adaptation |
| topic | Neural and Evolutionary Computing Optimization and Control |
| url | https://arxiv.org/abs/2401.15876 |