Variational Bayesian Methods for Stochastically Constrained System Design Problems

Prateek Jaiswal, Harsh Honnappa, Vinayak A. Rao
Proceedings of The 2nd Symposium on Advances in Approximate Bayesian Inference, PMLR 118:1-12, 2020.

Abstract

We study system design problems stated as parameterized stochastic programs with a chance-constraint set. We adopt a Bayesian approach that requires the computation of a posterior predictive integral which is usually intractable. In addition, for the problem to be a well-dened convex program, we must retain the convexity of the feasible set. Consequently, we propose a variational Bayes-based method to approximately compute the posterior predictive integral that ensures tractability and retains the convexity of the feasible set. Under certain regularity conditions, we also show that the solution set obtained using variational Bayes converges to the true solution set as the number of observations tends to infinity. We also provide bounds on the probability of qualifying a true infeasible point (with respect to the true constraints) as feasible under the VB approximation for a given number of samples.

Cite this Paper

BibTeX
@InProceedings{pmlr-v118-jaiswal20a, title = { Variational Bayesian Methods for Stochastically Constrained System Design Problems}, author = {Jaiswal, Prateek and Honnappa, Harsh and Rao, Vinayak A.}, booktitle = {Proceedings of The 2nd Symposium on Advances in Approximate Bayesian Inference}, pages = {1--12}, year = {2020}, editor = {Zhang, Cheng and Ruiz, Francisco and Bui, Thang and Dieng, Adji Bousso and Liang, Dawen}, volume = {118}, series = {Proceedings of Machine Learning Research}, month = {08 Dec}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v118/jaiswal20a/jaiswal20a.pdf}, url = {https://proceedings.mlr.press/v118/jaiswal20a.html}, abstract = { We study system design problems stated as parameterized stochastic programs with a chance-constraint set. We adopt a Bayesian approach that requires the computation of a posterior predictive integral which is usually intractable. In addition, for the problem to be a well-dened convex program, we must retain the convexity of the feasible set. Consequently, we propose a variational Bayes-based method to approximately compute the posterior predictive integral that ensures tractability and retains the convexity of the feasible set. Under certain regularity conditions, we also show that the solution set obtained using variational Bayes converges to the true solution set as the number of observations tends to infinity. We also provide bounds on the probability of qualifying a true infeasible point (with respect to the true constraints) as feasible under the VB approximation for a given number of samples.} }
Endnote
%0 Conference Paper %T Variational Bayesian Methods for Stochastically Constrained System Design Problems %A Prateek Jaiswal %A Harsh Honnappa %A Vinayak A. Rao %B Proceedings of The 2nd Symposium on Advances in Approximate Bayesian Inference %C Proceedings of Machine Learning Research %D 2020 %E Cheng Zhang %E Francisco Ruiz %E Thang Bui %E Adji Bousso Dieng %E Dawen Liang %F pmlr-v118-jaiswal20a %I PMLR %P 1--12 %U https://proceedings.mlr.press/v118/jaiswal20a.html %V 118 %X We study system design problems stated as parameterized stochastic programs with a chance-constraint set. We adopt a Bayesian approach that requires the computation of a posterior predictive integral which is usually intractable. In addition, for the problem to be a well-dened convex program, we must retain the convexity of the feasible set. Consequently, we propose a variational Bayes-based method to approximately compute the posterior predictive integral that ensures tractability and retains the convexity of the feasible set. Under certain regularity conditions, we also show that the solution set obtained using variational Bayes converges to the true solution set as the number of observations tends to infinity. We also provide bounds on the probability of qualifying a true infeasible point (with respect to the true constraints) as feasible under the VB approximation for a given number of samples.
APA
Jaiswal, P., Honnappa, H. & Rao, V.A.. (2020). Variational Bayesian Methods for Stochastically Constrained System Design Problems. Proceedings of The 2nd Symposium on Advances in Approximate Bayesian Inference, in Proceedings of Machine Learning Research 118:1-12 Available from https://proceedings.mlr.press/v118/jaiswal20a.html.

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