← 研踪 PaperTrailarXiv:2611.14883 · v1
Random feature policy iteration for inverse mean field games with complex geometry and high dimensions
首次提交 2026-11-11 09:18
版本更新 2026-11-11 09:18
雷达观测 2026-11-13 10:09
摘要
We propose a random feature policy iteration method for reconstructing the obstacle function in a mean-field game (MFG) from observations of its value function, leveraging the method's mesh-free nature and flexibility to handle complex geometries and high-dimensional problems. The method builds on a policy iteration framework for inverse MFGs, which decouples the coupled nonlinear forward-backward PDE system into a sequence of linear PDE and inverse problem solves. The fixed random feature representations preserve this linear structure, allowing the resulting subproblems to be solved by minimizing residuals at sampled collocation points through linear least-squares problems. The mesh-free nature of the method further extends the applicability of the policy iteration framework to inverse MFGs with complex geometry and in high dimensions. Another key advantage is its flexibility in using different spatial approximations for different variables: the obstacle function, value function, and population density can be represented in separate feature spaces, accommodating obstacles that are substantially less regular than the corresponding PDE solutions. Moreover, boundary conditions can be enforced through collocation on irregular domains without constructing boundary-fitted meshes. Numerical experiments involving smooth and discontinuous obstacles, a domain with holes, and higher-dimensional problems demonstrate the accuracy and flexibility of the proposed method.
作者备注：20 pages, 7 figures
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v1 · 2026-11-11 09:18 · 最新观测版本
Random feature policy iteration for inverse mean field games with complex geometry and high dimensions
We propose a random feature policy iteration method for reconstructing the obstacle function in a mean-field game (MFG) from observations of its value function, leveraging the method's mesh-free nature and flexibility to handle complex geometries and high-dimensional problems. The method builds on a policy iteration framework for inverse MFGs, which decouples the coupled nonlinear forward-backward PDE system into a sequence of linear PDE and inverse problem solves. The fixed random feature representations preserve this linear structure, allowing the resulting subproblems to be solved by minimizing residuals at sampled collocation points through linear least-squares problems. The mesh-free nature of the method further extends the applicability of the policy iteration framework to inverse MFGs with complex geometry and in high dimensions. Another key advantage is its flexibility in using different spatial approximations for different variables: the obstacle function, value function, and population density can be represented in separate feature spaces, accommodating obstacles that are substantially less regular than the corresponding PDE solutions. Moreover, boundary conditions can be enforced through collocation on irregular domains without constructing boundary-fitted meshes. Numerical experiments involving smooth and discontinuous obstacles, a domain with holes, and higher-dimensional problems demonstrate the accuracy and flexibility of the proposed method.
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