Sample Average Approximation for Alpha-Divergence Minimization with Exponential Convergence Guarantees

François Bertholom, François Roueff, Randal Douc
Proceedings of The 29th International Conference on Artificial Intelligence and Statistics, PMLR 300:1054-1062, 2026.

Abstract

We study the problem of approximating an unnormalized target distribution using probability densities from an exponential family. Specifically, we establish convergence guarantees for a monotonic alpha-divergence minimization algorithm, which decreases the alpha-divergence at each iteration. To illustrate our theoretical results, we propose an implementable Sample Average Approximation algorithm that solves a discrete approximation of the original problem. Through a detailed analysis of the loss landscape and the algorithm’s dynamics, we provide practical design guidelines which suffice to ensure its convergence.

Cite this Paper

BibTeX
@InProceedings{pmlr-v300-bertholom26a, title = { Sample Average Approximation for Alpha-Divergence Minimization with Exponential Convergence Guarantees }, author = {Bertholom, Fran{\c{c}}ois and Roueff, Fran{\c{c}}ois and Douc, Randal}, booktitle = {Proceedings of The 29th International Conference on Artificial Intelligence and Statistics}, pages = {1054--1062}, year = {2026}, editor = {Khan, Emtiyaz and Li, Yingzhen and Solin, Arno and Ramdas, Aaditya}, volume = {300}, series = {Proceedings of Machine Learning Research}, month = {02--05 May}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v300/main/assets/bertholom26a/bertholom26a.pdf}, url = {https://proceedings.mlr.press/v300/bertholom26a.html}, abstract = { We study the problem of approximating an unnormalized target distribution using probability densities from an exponential family. Specifically, we establish convergence guarantees for a monotonic alpha-divergence minimization algorithm, which decreases the alpha-divergence at each iteration. To illustrate our theoretical results, we propose an implementable Sample Average Approximation algorithm that solves a discrete approximation of the original problem. Through a detailed analysis of the loss landscape and the algorithm’s dynamics, we provide practical design guidelines which suffice to ensure its convergence. } }
Endnote
%0 Conference Paper %T Sample Average Approximation for Alpha-Divergence Minimization with Exponential Convergence Guarantees %A François Bertholom %A François Roueff %A Randal Douc %B Proceedings of The 29th International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2026 %E Emtiyaz Khan %E Yingzhen Li %E Arno Solin %E Aaditya Ramdas %F pmlr-v300-bertholom26a %I PMLR %P 1054--1062 %U https://proceedings.mlr.press/v300/bertholom26a.html %V 300 %X We study the problem of approximating an unnormalized target distribution using probability densities from an exponential family. Specifically, we establish convergence guarantees for a monotonic alpha-divergence minimization algorithm, which decreases the alpha-divergence at each iteration. To illustrate our theoretical results, we propose an implementable Sample Average Approximation algorithm that solves a discrete approximation of the original problem. Through a detailed analysis of the loss landscape and the algorithm’s dynamics, we provide practical design guidelines which suffice to ensure its convergence.
APA
Bertholom, F., Roueff, F. & Douc, R.. (2026). Sample Average Approximation for Alpha-Divergence Minimization with Exponential Convergence Guarantees . Proceedings of The 29th International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 300:1054-1062 Available from https://proceedings.mlr.press/v300/bertholom26a.html.

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