Assessing solution Quality in stochastic Optimization via bootstrap Aggregating

Henry Lam, Huajie Qian

Abstract: We study a statistical method to estimate the optimality gap, as an assessment of the quality, of a given solution for a stochastic optimization using limited data. Our approach is based on bootstrap aggregating the resampled optimal values of sample average approximation (SAA), by connecting these SAA values with the classical notion of symmetric statistics. We discuss how this approach works on general stochastic optimization problems and is statistically more efficient than some previous methods. We substantiate our findings with several numerical experiments.