Adaptive Tuning for Metropolis Adjusted Langevin Trajectories

Lionel Riou-Durand, Pavel Sountsov, Jure Vogrinc, Charles Margossian, Sam Power
Proceedings of The 26th International Conference on Artificial Intelligence and Statistics, PMLR 206:8102-8116, 2023.

Abstract

Hamiltonian Monte Carlo (HMC) is a widely used sampler for continuous probability distributions. In many cases, the underlying Hamiltonian dynamics exhibit a phenomenon of resonance which decreases the efficiency of the algorithm and makes it very sensitive to hyperparameter values. This issue can be tackled efficiently, either via the use of trajectory length randomization (RHMC) or via partial momentum refreshment. The second approach is connected to the kinetic Langevin diffusion, and has been mostly investigated through the use of Generalized HMC (GHMC). However, GHMC induces momentum flips upon rejections causing the sampler to backtrack and waste computational resources. In this work we focus on a recent algorithm bypassing this issue, named Metropolis Adjusted Langevin Trajectories (MALT). We build upon recent strategies for tuning the hyperparameters of RHMC which target a bound on the Effective Sample Size (ESS) and adapt it to MALT, thereby enabling the first user-friendly deployment of this algorithm. We construct a method to optimize a sharper bound on the ESS and reduce the estimator variance. Easily compatible with parallel implementation, the resultant Adaptive MALT algorithm is competitive in terms of ESS rate and hits useful tradeoffs in memory usage when compared to GHMC, RHMC and NUTS.

Cite this Paper

BibTeX
@InProceedings{pmlr-v206-riou-durand23a, title = {Adaptive Tuning for Metropolis Adjusted Langevin Trajectories}, author = {Riou-Durand, Lionel and Sountsov, Pavel and Vogrinc, Jure and Margossian, Charles and Power, Sam}, booktitle = {Proceedings of The 26th International Conference on Artificial Intelligence and Statistics}, pages = {8102--8116}, year = {2023}, editor = {Ruiz, Francisco and Dy, Jennifer and van de Meent, Jan-Willem}, volume = {206}, series = {Proceedings of Machine Learning Research}, month = {25--27 Apr}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v206/riou-durand23a/riou-durand23a.pdf}, url = {https://proceedings.mlr.press/v206/riou-durand23a.html}, abstract = {Hamiltonian Monte Carlo (HMC) is a widely used sampler for continuous probability distributions. In many cases, the underlying Hamiltonian dynamics exhibit a phenomenon of resonance which decreases the efficiency of the algorithm and makes it very sensitive to hyperparameter values. This issue can be tackled efficiently, either via the use of trajectory length randomization (RHMC) or via partial momentum refreshment. The second approach is connected to the kinetic Langevin diffusion, and has been mostly investigated through the use of Generalized HMC (GHMC). However, GHMC induces momentum flips upon rejections causing the sampler to backtrack and waste computational resources. In this work we focus on a recent algorithm bypassing this issue, named Metropolis Adjusted Langevin Trajectories (MALT). We build upon recent strategies for tuning the hyperparameters of RHMC which target a bound on the Effective Sample Size (ESS) and adapt it to MALT, thereby enabling the first user-friendly deployment of this algorithm. We construct a method to optimize a sharper bound on the ESS and reduce the estimator variance. Easily compatible with parallel implementation, the resultant Adaptive MALT algorithm is competitive in terms of ESS rate and hits useful tradeoffs in memory usage when compared to GHMC, RHMC and NUTS.} }
Endnote
%0 Conference Paper %T Adaptive Tuning for Metropolis Adjusted Langevin Trajectories %A Lionel Riou-Durand %A Pavel Sountsov %A Jure Vogrinc %A Charles Margossian %A Sam Power %B Proceedings of The 26th International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2023 %E Francisco Ruiz %E Jennifer Dy %E Jan-Willem van de Meent %F pmlr-v206-riou-durand23a %I PMLR %P 8102--8116 %U https://proceedings.mlr.press/v206/riou-durand23a.html %V 206 %X Hamiltonian Monte Carlo (HMC) is a widely used sampler for continuous probability distributions. In many cases, the underlying Hamiltonian dynamics exhibit a phenomenon of resonance which decreases the efficiency of the algorithm and makes it very sensitive to hyperparameter values. This issue can be tackled efficiently, either via the use of trajectory length randomization (RHMC) or via partial momentum refreshment. The second approach is connected to the kinetic Langevin diffusion, and has been mostly investigated through the use of Generalized HMC (GHMC). However, GHMC induces momentum flips upon rejections causing the sampler to backtrack and waste computational resources. In this work we focus on a recent algorithm bypassing this issue, named Metropolis Adjusted Langevin Trajectories (MALT). We build upon recent strategies for tuning the hyperparameters of RHMC which target a bound on the Effective Sample Size (ESS) and adapt it to MALT, thereby enabling the first user-friendly deployment of this algorithm. We construct a method to optimize a sharper bound on the ESS and reduce the estimator variance. Easily compatible with parallel implementation, the resultant Adaptive MALT algorithm is competitive in terms of ESS rate and hits useful tradeoffs in memory usage when compared to GHMC, RHMC and NUTS.
APA
Riou-Durand, L., Sountsov, P., Vogrinc, J., Margossian, C. & Power, S.. (2023). Adaptive Tuning for Metropolis Adjusted Langevin Trajectories. Proceedings of The 26th International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 206:8102-8116 Available from https://proceedings.mlr.press/v206/riou-durand23a.html.

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