Variational Bayesian Methods for Stochastically Constrained System Design Problems
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Proceedings of The 2nd Symposium on
Advances in Approximate Bayesian Inference, PMLR 118:112, 2020.
Abstract
We study system design problems stated as parameterized stochastic programs with a chanceconstraint 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 welldened convex program, we must retain the convexity of the feasible set. Consequently, we propose a variational Bayesbased 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.
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