تقرير
Natural Gradient Interpretation of Rank-One Update in CMA-ES
| العنوان: | Natural Gradient Interpretation of Rank-One Update in CMA-ES |
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| المؤلفون: | Hamano, Ryoki, Shirakawa, Shinichi, Nomura, Masahiro |
| سنة النشر: | 2024 |
| المجموعة: | Computer Science |
| مصطلحات موضوعية: | Computer Science - Neural and Evolutionary Computing |
| الوصف: | The covariance matrix adaptation evolution strategy (CMA-ES) is a stochastic search algorithm using a multivariate normal distribution for continuous black-box optimization. In addition to strong empirical results, part of the CMA-ES can be described by a stochastic natural gradient method and can be derived from information geometric optimization (IGO) framework. However, there are some components of the CMA-ES, such as the rank-one update, for which the theoretical understanding is limited. While the rank-one update makes the covariance matrix to increase the likelihood of generating a solution in the direction of the evolution path, this idea has been difficult to formulate and interpret as a natural gradient method unlike the rank-$\mu$ update. In this work, we provide a new interpretation of the rank-one update in the CMA-ES from the perspective of the natural gradient with prior distribution. First, we propose maximum a posteriori IGO (MAP-IGO), which is the IGO framework extended to incorporate a prior distribution. Then, we derive the rank-one update from the MAP-IGO by setting the prior distribution based on the idea that the promising mean vector should exist in the direction of the evolution path. Moreover, the newly derived rank-one update is extensible, where an additional term appears in the update for the mean vector. We empirically investigate the properties of the additional term using various benchmark functions. Comment: This paper has been accepted for presentation at PPSN2024. Updated experimental results and related sentences in Sections 6 and 7 |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2406.16506 |
| رقم الأكسشن: | edsarx.2406.16506 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |