Bayesian Joint Chance Constrained Optimization: Approximations and Statistical Consistency
研究了在贝叶斯框架下处理数据驱动的机会约束随机优化问题，证明了使用近似后验分布计算的最优值在频率学派意义下具有统计一致性，并给出了收敛速率和凸可行性，最后在M/M/c排队模型的人员配置问题上验证了方法。
This paper considers data-driven chance-constrained stochastic optimization problems in a Bayesian framework. Bayesian posteriors afford a principled mechanism to incorporate data and prior knowledge into stochastic optimization problems. However, the computation of Bayesian posteriors is typically an intractable problem, and has spawned a large literature on approximate Bayesian computation. Here, in the context of chance-constrained optimization, we focus on the question of statistical consistency (in an appropriate sense) of the optimal value, computed using an approximate posterior distribution. To this end, we rigorously prove a frequentist consistency result demonstrating the convergence of the optimal value to the optimal value of a fixed, parameterized constrained optimization problem. We augment this by also establishing a probabilistic rate of convergence of the optimal value. We also prove the convex feasibility of the approximate Bayesian stochastic optimization problem. Finally, we demonstrate the utility of our approach on an optimal staffing problem for an M/M/c queueing model.