Concentration of Measure for Chance-Constrained Optimization

Authors: Sadegh Soudjani and Rupak Majumdar

Paper Information

Title:Concentration of Measure for Chance-Constrained Optimization
Authors:Sadegh Soudjani and Rupak Majumdar
Proceedings:ADHS Full papers
Editor: Alessandro Abate
Keywords:aaa, bbb, ccc

ABSTRACT. Chance-constrained optimization problems optimize a cost function in the presence of probabilistic constraints. They are convex in very special cases and, in practice, they are solved using approximation techniques. In this paper, we study approximation of chance constraints for the class of probability distributions that satisfy a concentration of measure property. We show that using concentration of measure, we can transform chance constraints to constraints on expectations, which can then be solved based on scenario optimization. Our approach depends solely on the concentration of measure property of the uncertainty and does not require the objective or constraint functions to be convex. We also give bounds on the required number of scenarios for achieving a certain confidence. We demonstrate our approach on a non-convex chanced-constrained optimization, and benchmark our technique against alternative approaches in the literature on chance-constrained LQG problem.

Talk:Jul 13 11:40 (Session 85: Stochastic systems 2)