论文标题
用于随机约束的系统设计问题的变异贝叶斯方法
Variational Bayesian Methods for Stochastically Constrained System Design Problems
论文作者
论文摘要
我们研究了具有Change-Constraint集合的参数化随机程序的系统设计问题。我们采用一种贝叶斯方法，需要计算后验预测积分，这通常是棘手的。此外，要使问题是一个定义明确的凸面程序，我们必须保留可行集合的凸度。因此，我们提出了一种基于差异的贝叶斯方法，以大致计算后验预测积分，以确保可行设置的障碍性并保留凸的性能。在某些规律性条件下，我们还表明，随着观测值的数量倾向于无穷大，使用变分贝叶斯获得的解决方案集会收敛到真实溶液集。我们还为给定数量的样本在VB近似中可行的限定限定真正不可行的点（相对于真实约束）的概率提供了界限。
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-defined 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.
