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| Auteurs principaux: | , , , , , , |
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| Format: | Preprint |
| Publié: |
2025
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| Sujets: | |
| Accès en ligne: | https://arxiv.org/abs/2508.12511 |
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| _version_ | 1866917339707998208 |
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| author | Blessing, Denis Berner, Julius Richter, Lorenz Domingo-Enrich, Carles Du, Yuanqi Vahdat, Arash Neumann, Gerhard |
| author_facet | Blessing, Denis Berner, Julius Richter, Lorenz Domingo-Enrich, Carles Du, Yuanqi Vahdat, Arash Neumann, Gerhard |
| contents | Solving stochastic optimal control problems with quadratic control costs can be viewed as approximating a target path space measure, e.g. via gradient-based optimization. In practice, however, this optimization is challenging in particular if the target measure differs substantially from the prior. In this work, we therefore approach the problem by iteratively solving constrained problems incorporating trust regions that aim for approaching the target measure gradually in a systematic way. It turns out that this trust region based strategy can be understood as a geometric annealing from the prior to the target measure, where, however, the incorporated trust regions lead to a principled and educated way of choosing the time steps in the annealing path. We demonstrate in multiple optimal control applications that our novel method can improve performance significantly, including tasks in diffusion-based sampling, transition path sampling, and fine-tuning of diffusion models. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_12511 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Trust Region Constrained Measure Transport in Path Space for Stochastic Optimal Control and Inference Blessing, Denis Berner, Julius Richter, Lorenz Domingo-Enrich, Carles Du, Yuanqi Vahdat, Arash Neumann, Gerhard Machine Learning Solving stochastic optimal control problems with quadratic control costs can be viewed as approximating a target path space measure, e.g. via gradient-based optimization. In practice, however, this optimization is challenging in particular if the target measure differs substantially from the prior. In this work, we therefore approach the problem by iteratively solving constrained problems incorporating trust regions that aim for approaching the target measure gradually in a systematic way. It turns out that this trust region based strategy can be understood as a geometric annealing from the prior to the target measure, where, however, the incorporated trust regions lead to a principled and educated way of choosing the time steps in the annealing path. We demonstrate in multiple optimal control applications that our novel method can improve performance significantly, including tasks in diffusion-based sampling, transition path sampling, and fine-tuning of diffusion models. |
| title | Trust Region Constrained Measure Transport in Path Space for Stochastic Optimal Control and Inference |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2508.12511 |