  We explore generalizations of some integrated learning and optimization
frameworks for data-driven contextual stochastic optimization that can adapt to
heteroscedasticity. We identify conditions on the stochastic program, data
generation process, and the prediction setup under which these generalizations
possess asymptotic and finite sample guarantees for a class of stochastic
programs, including two-stage stochastic mixed-integer programs with continuous
recourse. We verify that our assumptions hold for popular parametric and
nonparametric regression methods.
