Distributionally robust stochastic programs with side information based on trimmings

摘要: We consider stochastic programs conditional on some covariate information, where the only knowledge of possible relationship between uncertain parameters and covariates is reduced to a finite data sample their joint distribution. By exploiting close link notion trimmings probability measure partial mass transportation problem, we construct data-driven Distributionally Robust Optimization (DRO) framework hedge decision against intrinsic error in process inferring information from limited data. show that our approach computationally as tractable standard (without side information) Wasserstein-metric-based DRO. Furthermore, DRO can be conveniently used address decision-making problems under contaminated samples naturally produces distributionally robust versions local nonparametric predictive methods, such Nadaraya-Watson kernel regression $K$-nearest neighbors, which are often context optimization. Leveraging results empirical point processes optimal transport, enjoys performance guarantees. Finally, theoretical illustrated using single-item newsvendor problem portfolio allocation with information.