标题： 变分贝叶斯方法用于随机约束系统设计问题 显示英文标题

标题： Variational Bayesian Methods for Stochastically Constrained System Design Problems

摘要： 我们研究作为带有概率约束集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，该方法需要计算一个后验预测积分，这通常难以处理。 此外，为了使问题成为定义良好的凸程序，我们必须保持可行集的凸性。 因此，我们提出一种变分贝叶斯方法，以近似计算后验预测积分，该方法确保可处理性并保持可行集的凸性。 在某些正则条件下，我们还证明了使用变分贝叶斯得到的解集随着观测数量趋于无穷大而收敛到真实解集。 我们还提供了在给定样本数量下，根据VB近似，将一个真实的不可行点（相对于真实约束）误判为可行点的概率的界限。 显示英文摘要

摘要： 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.