The paper discusses connections between the problems of the two-stage stochastic programming, robust decision making, robust statistical estimation and machine learning. In the conditions of uncertainty, possible extreme events and outliers, these problems require quantile-based criteria, constraints, and “goodness-of-fit” indicators. The two-stage STO problems with quantile-based criteria can be effectively solved with the iterative stochastic quasigradient (SQG) solution algorithms. The SQG methods provide a new type of machine learning algorithms that can be effectively used for general type nonsmooth, possibly discontinuous and nonconvex problems, including quantile regression and neural networks training. In general problems of decision-making, feasible solutions, concepts of optimality and robustness are characterized from the context of decision-making situations. Robust ML approaches can be integrated with disciplinary or interdisciplinary decision-making models, e.g., land use, agricultural, energy, etc., for robust decision-making in the conditions of uncertainty, increasing systemic interdependencies and “unknown risks”.