Stochastic optimization using Hellinger distance

Stochastic optimization facilitates decision making in uncertain environments. In typical problems, probability distributions are fit to historical data for the chance variables and then optimization is carried out, as if the estimated probability distributions are the “truth”. However, this perspective is optimistic in nature and can frequently lead to sub-optimal or infeasible results because the distribution can be misspecified and the historical data set may be contaminated. In this paper, we propose to integrate existing approaches to decision making under uncertainty with robust and efficient estimation procedures using Hellinger distance. Within the existing decision-making methodologies that make use of parametric models, our approach offers robustness against model misspecifications and data contamination. Additionally, it also facilitates quantification of the impact of uncertainty in historical data on optimization results.