Data-Driven Piecewise Affine Decision Rules for Stochastic Programming with Covariate Information

Piecewise affine decision rule methods enable the smarter and more efficient decision making for contextual stochastic programming In contextual stochastic programming, the efficacy of data-driven decision rule (DR) methods often faces the trade-off between approximation accuracy of DR hypothesis class and computational efficiency of learning the DR. To this end, in “Data-driven Piecewise Affine Decision Rules for Stochastic Programming with Covariate Information,” Zhang, Liu, and Zhao employ a piecewise affine decision rule (PADR) characterized by the difference of max-affine formula. Their research shows the consistency guarantees of the PADR method with the excess risk bound without the assumption of convexity or linearity. By exploiting the compact max-affine structure of PADR, they develop a novel majorization-minimization algorithm to efficiently solve the highly nonconvex and nonsmooth PADR-based ERM problem. Numerical experiments show that PADR significantly lowers costs, decreases computation time, and is robust to feature dimensions and nonlinearity of the underlying dependency. These results offers a theoretically consistent and practically scalable PADR approach for researchers and practitioners to solve contextual stochastic programming with both high reliability and computational efficiency.