Tamed Langevin sampling under weaker conditions

Iosif Lytras, Panayotis Mertikopoulos
Proceedings of The 28th International Conference on Artificial Intelligence and Statistics, PMLR 258:847-855, 2025.

Abstract

Motivated by applications to deep learning which often fail standard Lipschitz smoothness requirements, we examine the problem of sampling from distributions that are not log-concave and are only weakly dissipative, with log-gradients allowed to grow superlinearly at infinity. In terms of structure, we only assume that the target distribution satisfies either a Log-Sobolev or a Poincare inequality and a local Lipschitz smoothness assumption with modulus growing possibly polynomially at infinity. This set of assumptions greatly exceeds the operational limits of the "vanilla" ULA, making sampling from such distributions a highly involved affair. To account for this, we introduce a taming scheme which is tailored to the growth and decay properties of the target distribution, and we provide explicit non-asymptotic guarantees for the proposed sampler in terms of the KL divergence, total variation, and Wasserstein distance to the target distribution.

Cite this Paper

BibTeX
@InProceedings{pmlr-v258-lytras25a, title = {Tamed Langevin sampling under weaker conditions}, author = {Lytras, Iosif and Mertikopoulos, Panayotis}, booktitle = {Proceedings of The 28th International Conference on Artificial Intelligence and Statistics}, pages = {847--855}, year = {2025}, editor = {Li, Yingzhen and Mandt, Stephan and Agrawal, Shipra and Khan, Emtiyaz}, volume = {258}, series = {Proceedings of Machine Learning Research}, month = {03--05 May}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v258/main/assets/lytras25a/lytras25a.pdf}, url = {https://proceedings.mlr.press/v258/lytras25a.html}, abstract = {Motivated by applications to deep learning which often fail standard Lipschitz smoothness requirements, we examine the problem of sampling from distributions that are not log-concave and are only weakly dissipative, with log-gradients allowed to grow superlinearly at infinity. In terms of structure, we only assume that the target distribution satisfies either a Log-Sobolev or a Poincare inequality and a local Lipschitz smoothness assumption with modulus growing possibly polynomially at infinity. This set of assumptions greatly exceeds the operational limits of the "vanilla" ULA, making sampling from such distributions a highly involved affair. To account for this, we introduce a taming scheme which is tailored to the growth and decay properties of the target distribution, and we provide explicit non-asymptotic guarantees for the proposed sampler in terms of the KL divergence, total variation, and Wasserstein distance to the target distribution.} }
Endnote
%0 Conference Paper %T Tamed Langevin sampling under weaker conditions %A Iosif Lytras %A Panayotis Mertikopoulos %B Proceedings of The 28th International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2025 %E Yingzhen Li %E Stephan Mandt %E Shipra Agrawal %E Emtiyaz Khan %F pmlr-v258-lytras25a %I PMLR %P 847--855 %U https://proceedings.mlr.press/v258/lytras25a.html %V 258 %X Motivated by applications to deep learning which often fail standard Lipschitz smoothness requirements, we examine the problem of sampling from distributions that are not log-concave and are only weakly dissipative, with log-gradients allowed to grow superlinearly at infinity. In terms of structure, we only assume that the target distribution satisfies either a Log-Sobolev or a Poincare inequality and a local Lipschitz smoothness assumption with modulus growing possibly polynomially at infinity. This set of assumptions greatly exceeds the operational limits of the "vanilla" ULA, making sampling from such distributions a highly involved affair. To account for this, we introduce a taming scheme which is tailored to the growth and decay properties of the target distribution, and we provide explicit non-asymptotic guarantees for the proposed sampler in terms of the KL divergence, total variation, and Wasserstein distance to the target distribution.
APA
Lytras, I. & Mertikopoulos, P.. (2025). Tamed Langevin sampling under weaker conditions. Proceedings of The 28th International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 258:847-855 Available from https://proceedings.mlr.press/v258/lytras25a.html.

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