تقرير
Deep neural network approximation for high-dimensional parabolic Hamilton-Jacobi-Bellman equations
| العنوان: | Deep neural network approximation for high-dimensional parabolic Hamilton-Jacobi-Bellman equations |
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| المؤلفون: | Grohs, Philipp, Herrmann, Lukas |
| سنة النشر: | 2021 |
| المجموعة: | Computer Science Mathematics Statistics |
| مصطلحات موضوعية: | Mathematics - Numerical Analysis, Computer Science - Machine Learning, Statistics - Machine Learning, 65C99, 65M99, 60H30 |
| الوصف: | The approximation of solutions to second order Hamilton--Jacobi--Bellman (HJB) equations by deep neural networks is investigated. It is shown that for HJB equations that arise in the context of the optimal control of certain Markov processes the solution can be approximated by deep neural networks without incurring the curse of dimension. The dynamics is assumed to depend affinely on the controls and the cost depends quadratically on the controls. The admissible controls take values in a bounded set. |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2103.05744 |
| رقم الأكسشن: | edsarx.2103.05744 |
| قاعدة البيانات: | arXiv |
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