Communication Dans Un Congrès Année : 2020

Penalized Langevin dynamics with vanishing penalty for smooth and log-concave targets

Résumé

We study the problem of sampling from a probability distribution on $\mathbb R^p$ defined via a convex and smooth potential function. We consider a continuous-time diffusion-type process, termed Penalized Langevin dynamics (PLD), the drift of which is the negative gradient of the potential plus a linear penalty that vanishes when time goes to infinity. An upper bound on the Wasserstein-2 distance between the distribution of the PLD at time $t$ and the target is established. This upper bound highlights the influence of the speed of decay of the penalty on the accuracy of the approximation. As a consequence, considering the low-temperature limit we infer a new nonasymptotic guarantee of convergence of the penalized gradient flow for the optimization problem.

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Dates et versions

hal-04901582 , version 1 (20-01-2025)

Identifiants

Citer

Avetik Karagulyan, Arnak Dalalyan. Penalized Langevin dynamics with vanishing penalty for smooth and log-concave targets. Neural Information Processing Systems, Dec 2020, Vancouver (BC), Canada. pp.17594-17604, ⟨10.48550/arXiv.2006.13998⟩. ⟨hal-04901582⟩
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