A deep learning algorithm for computing mean field control problems via forward-backward score dynamics
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2024
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866918022365577216 |
|---|---|
| author | Zhou, Mo Osher, Stanley Li, Wuchen |
| author_facet | Zhou, Mo Osher, Stanley Li, Wuchen |
| contents | We propose a deep learning approach to compute mean field control problems with individual noises. The problem consists of the Fokker-Planck (FP) equation and the Hamilton-Jacobi-Bellman (HJB) equation. Using the differential of the entropy, namely the score function, we first formulate the deterministic forward-backward characteristics for the mean field control system, which is different from the classical forward-backward stochastic differential equations (FBSDEs). We further apply the neural network approximation to fit the proposed deterministic characteristic lines. Numerical examples, including the control problem with entropy potential energy, the linear quadratic regulator, and the systemic risks, demonstrate the effectiveness of the proposed method. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_09547 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A deep learning algorithm for computing mean field control problems via forward-backward score dynamics Zhou, Mo Osher, Stanley Li, Wuchen Optimization and Control 49N80 (Primary) 35Q89 (Secondary) G.1.6; G.1.8 We propose a deep learning approach to compute mean field control problems with individual noises. The problem consists of the Fokker-Planck (FP) equation and the Hamilton-Jacobi-Bellman (HJB) equation. Using the differential of the entropy, namely the score function, we first formulate the deterministic forward-backward characteristics for the mean field control system, which is different from the classical forward-backward stochastic differential equations (FBSDEs). We further apply the neural network approximation to fit the proposed deterministic characteristic lines. Numerical examples, including the control problem with entropy potential energy, the linear quadratic regulator, and the systemic risks, demonstrate the effectiveness of the proposed method. |
| title | A deep learning algorithm for computing mean field control problems via forward-backward score dynamics |
| topic | Optimization and Control 49N80 (Primary) 35Q89 (Secondary) G.1.6; G.1.8 |
| url | https://arxiv.org/abs/2401.09547 |