Forward-KL Convergence of Time-Inhomogeneous Langevin Diffusions
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866909032490467328 |
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| author | Habring, Andreas Zach, Martin |
| author_facet | Habring, Andreas Zach, Martin |
| contents | Many practical samplers rely on time-dependent drifts -- often induced by annealing or tempering schedules -- to improve exploration and stability. This motivates a unified non-asymptotic analysis of the corresponding Langevin diffusions and their discretizations. We provide a convergence analysis that includes non-asymptotic bounds for the continuous-time diffusion and its Euler--Maruyama discretization in the forward-Kullback--Leibler divergence under a single set of abstract conditions on the time-dependent drift. The results apply to many practically-relevant annealing schemes, including geometric tempering and annealed Langevin sampling. In addition, we provide numerical experiments comparing the annealing schemes covered by our theory in low- and high-dimensional settings. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2601_22349 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Forward-KL Convergence of Time-Inhomogeneous Langevin Diffusions Habring, Andreas Zach, Martin Numerical Analysis Optimization and Control 65C40, 65C05, 68U10, 65C60 G.3; I.4.5 Many practical samplers rely on time-dependent drifts -- often induced by annealing or tempering schedules -- to improve exploration and stability. This motivates a unified non-asymptotic analysis of the corresponding Langevin diffusions and their discretizations. We provide a convergence analysis that includes non-asymptotic bounds for the continuous-time diffusion and its Euler--Maruyama discretization in the forward-Kullback--Leibler divergence under a single set of abstract conditions on the time-dependent drift. The results apply to many practically-relevant annealing schemes, including geometric tempering and annealed Langevin sampling. In addition, we provide numerical experiments comparing the annealing schemes covered by our theory in low- and high-dimensional settings. |
| title | Forward-KL Convergence of Time-Inhomogeneous Langevin Diffusions |
| topic | Numerical Analysis Optimization and Control 65C40, 65C05, 68U10, 65C60 G.3; I.4.5 |
| url | https://arxiv.org/abs/2601.22349 |