Bayesian Joint Chance Constrained Optimization: Approximations and Statistical Consistency

This paper considers data-driven chance-constrained stochastic optimization problems in a Bayesian framework. posteriors afford principled mechanism to incorporate data and prior knowledge into problems. However, the computation of is typically an intractable problem, has spawned large literature on approximate computation. Here, context optimization, we focus question statistical consistency (in appropriate sense) optimal value, computed using posterior distribution. To this end, rigorously prove frequentist result demonstrating convergence value fixed, parameterized constrained problem. We augment by also establishing probabilistic rate value. convex feasibility Finally, demonstrate utility our approach staffing problem for M/M/c queueing model.