Score-based Metropolis-Hastings for Fractional Langevin Algorithms

• URL: http://arxiv.org/abs/2602.00835v1
• Date: Sat, 31 Jan 2026 17:59:22 GMT
• Title: Score-based Metropolis-Hastings for Fractional Langevin Algorithms
• Authors: Ahmed Aloui, Junyi Liao, Ali Hasan, Jose Blanchet, Vahid Tarokh,
• Abstract summary: We introduce the Metropolis-Adjusted Fractional Langevin Algorithm (MAFLA), an MH-inspired, fully score-based correction mechanism.<n>We show that MAFLA significantly improves finite time sampling accuracy over unadjusted fractional Langevin dynamics.
• Score: 13.572557872292
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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.

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