Score-based Metropolis-Hastings for Fractional Langevin Algorithms
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arXiv
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| Auteurs principaux: | , , , , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866910007538221056 |
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| author | Aloui, Ahmed Liao, Junyi Hasan, Ali Blanchet, Jose Tarokh, Vahid |
| author_facet | Aloui, Ahmed Liao, Junyi Hasan, Ali Blanchet, Jose Tarokh, Vahid |
| contents | Sampling from heavy-tailed and multimodal distributions is challenging when neither the target density nor the proposal density can be evaluated, as in $α$-stable Lévy-driven fractional Langevin algorithms. While the target distribution can be estimated from data via score-based or energy-based models, the $α$-stable proposal density and its score are generally unavailable, rendering classical density-based Metropolis--Hastings (MH) corrections impractical. Consequently, existing fractional Langevin methods operate in an unadjusted regime and can exhibit substantial finite-time errors and poor empirical control of tail behavior. We introduce the Metropolis-Adjusted Fractional Langevin Algorithm (MAFLA), an MH-inspired, fully score-based correction mechanism. MAFLA employs designed proxies for fractional proposal score gradients under isotropic symmetric $α$-stable noise and learns an acceptance function via Score Balance Matching. We empirically illustrate the strong performance of MAFLA on a series of tasks including combinatorial optimization problems where the method significantly improves finite time sampling accuracy over unadjusted fractional Langevin dynamics. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_00835 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Score-based Metropolis-Hastings for Fractional Langevin Algorithms Aloui, Ahmed Liao, Junyi Hasan, Ali Blanchet, Jose Tarokh, Vahid Machine Learning Sampling from heavy-tailed and multimodal distributions is challenging when neither the target density nor the proposal density can be evaluated, as in $α$-stable Lévy-driven fractional Langevin algorithms. While the target distribution can be estimated from data via score-based or energy-based models, the $α$-stable proposal density and its score are generally unavailable, rendering classical density-based Metropolis--Hastings (MH) corrections impractical. Consequently, existing fractional Langevin methods operate in an unadjusted regime and can exhibit substantial finite-time errors and poor empirical control of tail behavior. We introduce the Metropolis-Adjusted Fractional Langevin Algorithm (MAFLA), an MH-inspired, fully score-based correction mechanism. MAFLA employs designed proxies for fractional proposal score gradients under isotropic symmetric $α$-stable noise and learns an acceptance function via Score Balance Matching. We empirically illustrate the strong performance of MAFLA on a series of tasks including combinatorial optimization problems where the method significantly improves finite time sampling accuracy over unadjusted fractional Langevin dynamics. |
| title | Score-based Metropolis-Hastings for Fractional Langevin Algorithms |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2602.00835 |