Physics-informed approach for exploratory Hamilton--Jacobi--Bellman equations via policy iterations
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866915619628122112 |
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| author | Kim, Yeongjong Cho, Namkyeong Kim, Minseok Kim, Yeoneung |
| author_facet | Kim, Yeongjong Cho, Namkyeong Kim, Minseok Kim, Yeoneung |
| contents | We propose a mesh-free policy iteration framework based on physics-informed neural networks (PINNs) for solving entropy-regularized stochastic control problems. The method iteratively alternates between soft policy evaluation and improvement using automatic differentiation and neural approximation, without relying on spatial discretization. We present a detailed $L^2$ error analysis that decomposes the total approximation error into three sources: iteration error, policy network error, and PDE residual error. The proposed algorithm is validated with a range of challenging control tasks, including high-dimensional linear-quadratic regulation in 5D and 10D, as well as nonlinear systems such as pendulum and cartpole problems. Numerical results confirm the scalability, accuracy, and robustness of our approach across both linear and nonlinear benchmarks. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_01720 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Physics-informed approach for exploratory Hamilton--Jacobi--Bellman equations via policy iterations Kim, Yeongjong Cho, Namkyeong Kim, Minseok Kim, Yeoneung Numerical Analysis 93E20, 35Q93, 68T07 We propose a mesh-free policy iteration framework based on physics-informed neural networks (PINNs) for solving entropy-regularized stochastic control problems. The method iteratively alternates between soft policy evaluation and improvement using automatic differentiation and neural approximation, without relying on spatial discretization. We present a detailed $L^2$ error analysis that decomposes the total approximation error into three sources: iteration error, policy network error, and PDE residual error. The proposed algorithm is validated with a range of challenging control tasks, including high-dimensional linear-quadratic regulation in 5D and 10D, as well as nonlinear systems such as pendulum and cartpole problems. Numerical results confirm the scalability, accuracy, and robustness of our approach across both linear and nonlinear benchmarks. |
| title | Physics-informed approach for exploratory Hamilton--Jacobi--Bellman equations via policy iterations |
| topic | Numerical Analysis 93E20, 35Q93, 68T07 |
| url | https://arxiv.org/abs/2508.01720 |