Data-Driven Tuning for Chance-Constrained Optimization: Two Steps Towards Probabilistic Performance Guarantees

Abstract

Parameters involved in the formulation of optimization problems are often partially unknown or random. A popular way to mitigate the effect of uncertainty is using joint chance constraints, which guarantee constraint satisfaction with high probability but are challenging to solve. In this letter, we analyze an approach for joint chance constrained problems that involves iteratively tuning problem parameters. We first show that existing naive approaches to tuning can lead to solutions without feasibility guarantees. We then introduce a two-step approach, where a tuning-based solution generation step is followed by an a posteriori solution verification step. A main challenge of the two-step approach is to guarantee that the solution generated in the first step has a high probability of being verified as feasible in the second step. We therefore analyze how the relationship between the feasibility criteria used in each step impacts the probability of obtaining a feasible solution. We demonstrate our results in a numerical case study of the optimal power flow problem.