Adaptive Importance Sampling meets Mirror Descent : a Bias-variance Tradeoff

Anna Korba, François Portier
Proceedings of The 25th International Conference on Artificial Intelligence and Statistics, PMLR 151:11503-11527, 2022.

Abstract

Adaptive importance sampling is a widely spread Monte Carlo technique that uses a re-weighting strategy to iteratively estimate the so-called target distribution. A major drawback of adaptive importance sampling is the large variance of the weights which is known to badly impact the accuracy of the estimates. This paper investigates a regularization strategy whose basic principle is to raise the importance weights at a certain power. This regularization parameter, that might evolve between zero and one during the algorithm, is shown (i) to balance between the bias and the variance and (ii) to be connected to the mirror descent framework. Using a kernel density estimate to build the sampling policy, the uniform convergence is established under mild conditions. Finally, several practical ways to choose the regularization parameter are discussed and the benefits of the proposed approach are illustrated empirically.

Cite this Paper

BibTeX
@InProceedings{pmlr-v151-korba22a, title = { Adaptive Importance Sampling meets Mirror Descent : a Bias-variance Tradeoff }, author = {Korba, Anna and Portier, Fran\c{c}ois}, booktitle = {Proceedings of The 25th International Conference on Artificial Intelligence and Statistics}, pages = {11503--11527}, year = {2022}, editor = {Camps-Valls, Gustau and Ruiz, Francisco J. R. and Valera, Isabel}, volume = {151}, series = {Proceedings of Machine Learning Research}, month = {28--30 Mar}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v151/korba22a/korba22a.pdf}, url = {https://proceedings.mlr.press/v151/korba22a.html}, abstract = { Adaptive importance sampling is a widely spread Monte Carlo technique that uses a re-weighting strategy to iteratively estimate the so-called target distribution. A major drawback of adaptive importance sampling is the large variance of the weights which is known to badly impact the accuracy of the estimates. This paper investigates a regularization strategy whose basic principle is to raise the importance weights at a certain power. This regularization parameter, that might evolve between zero and one during the algorithm, is shown (i) to balance between the bias and the variance and (ii) to be connected to the mirror descent framework. Using a kernel density estimate to build the sampling policy, the uniform convergence is established under mild conditions. Finally, several practical ways to choose the regularization parameter are discussed and the benefits of the proposed approach are illustrated empirically. } }
Endnote
%0 Conference Paper %T Adaptive Importance Sampling meets Mirror Descent : a Bias-variance Tradeoff %A Anna Korba %A François Portier %B Proceedings of The 25th International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2022 %E Gustau Camps-Valls %E Francisco J. R. Ruiz %E Isabel Valera %F pmlr-v151-korba22a %I PMLR %P 11503--11527 %U https://proceedings.mlr.press/v151/korba22a.html %V 151 %X Adaptive importance sampling is a widely spread Monte Carlo technique that uses a re-weighting strategy to iteratively estimate the so-called target distribution. A major drawback of adaptive importance sampling is the large variance of the weights which is known to badly impact the accuracy of the estimates. This paper investigates a regularization strategy whose basic principle is to raise the importance weights at a certain power. This regularization parameter, that might evolve between zero and one during the algorithm, is shown (i) to balance between the bias and the variance and (ii) to be connected to the mirror descent framework. Using a kernel density estimate to build the sampling policy, the uniform convergence is established under mild conditions. Finally, several practical ways to choose the regularization parameter are discussed and the benefits of the proposed approach are illustrated empirically.
APA
Korba, A. & Portier, F.. (2022). Adaptive Importance Sampling meets Mirror Descent : a Bias-variance Tradeoff . Proceedings of The 25th International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 151:11503-11527 Available from https://proceedings.mlr.press/v151/korba22a.html.

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