تقرير
Convergence analysis of controlled particle systems arising in deep learning: from finite to infinite sample size
| العنوان: | Convergence analysis of controlled particle systems arising in deep learning: from finite to infinite sample size |
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| المؤلفون: | Liao, Huafu, Mészáros, Alpár R., Mou, Chenchen, Zhou, Chao |
| سنة النشر: | 2024 |
| المجموعة: | Computer Science Mathematics Statistics |
| مصطلحات موضوعية: | Mathematics - Optimization and Control, Computer Science - Machine Learning, Mathematics - Probability, Statistics - Machine Learning, 49N80, 65C35, 49L12, 62M45 |
| الوصف: | This paper deals with a class of neural SDEs and studies the limiting behavior of the associated sampled optimal control problems as the sample size grows to infinity. The neural SDEs with N samples can be linked to the N-particle systems with centralized control. We analyze the Hamilton--Jacobi--Bellman equation corresponding to the N-particle system and establish regularity results which are uniform in N. The uniform regularity estimates are obtained by the stochastic maximum principle and the analysis of a backward stochastic Riccati equation. Using these uniform regularity results, we show the convergence of the minima of objective functionals and optimal parameters of the neural SDEs as the sample size N tends to infinity. The limiting objects can be identified with suitable functions defined on the Wasserstein space of Borel probability measures. Furthermore, quantitative algebraic convergence rates are also obtained. Comment: 45 pages, 2 figures |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2404.05185 |
| رقم الأكسشن: | edsarx.2404.05185 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |