Mean field control with stopping
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866912977666441216 |
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| author | Cardaliaguet, Pierre Jackson, Joe Souganidis, Panagiotis E. |
| author_facet | Cardaliaguet, Pierre Jackson, Joe Souganidis, Panagiotis E. |
| contents | We study a high-dimensional stochastic optimization problem which features both control and stopping. In particular, a central planner steers a large population of particles, and can also remove particles at any time by paying a penalty. In the limit, we obtain a mean field control problem with discontinuous dynamics, in the sense that the controlled Fokker-Planck equation can have jumps. The value of the N-particle problem is characterized by a hierarchy of non-linear obstacle problems. The value of the limiting problem, meanwhile, solves an infinite-dimensional quasi-variational inequality (QVI). We introduce a notion of viscosity solution for this QVI, and obtain a comparison principle. Together with various regularity estimates, this comparison principle allows us to characterize the mean field value function as the unique viscosity solution of the QVI, and to establish the convergence of the N-particle value functions to the mean field value function. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_21204 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Mean field control with stopping Cardaliaguet, Pierre Jackson, Joe Souganidis, Panagiotis E. Optimization and Control Analysis of PDEs 49N80, 49L25 We study a high-dimensional stochastic optimization problem which features both control and stopping. In particular, a central planner steers a large population of particles, and can also remove particles at any time by paying a penalty. In the limit, we obtain a mean field control problem with discontinuous dynamics, in the sense that the controlled Fokker-Planck equation can have jumps. The value of the N-particle problem is characterized by a hierarchy of non-linear obstacle problems. The value of the limiting problem, meanwhile, solves an infinite-dimensional quasi-variational inequality (QVI). We introduce a notion of viscosity solution for this QVI, and obtain a comparison principle. Together with various regularity estimates, this comparison principle allows us to characterize the mean field value function as the unique viscosity solution of the QVI, and to establish the convergence of the N-particle value functions to the mean field value function. |
| title | Mean field control with stopping |
| topic | Optimization and Control Analysis of PDEs 49N80, 49L25 |
| url | https://arxiv.org/abs/2603.21204 |