부산대학교 도서관

The authors discuss connections between the problems of 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 stochastic optimization (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 network training. In general problems of decision-making, feasible solutions and concepts of optimality and robustness are characterized from the context of decision-making situations. Robust machine learning (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.' Keywords: two-stage STO, robust decision-making and statistical estimation, robust quantile regression, machine learning, general problems of robust decision making, systemic risks, uncertainties.
INTRODUCTION Various problems of decision-making under uncertainty, statistics, big data analysis, artificial intelligence (AI) can be formulated or can be reduced to two-stage stochastic optimization (STO) problems. For example, these [...]