A Survey of Decision Making and Optimization under Uncertainty

Recent advances in decision making have incorporated both risk and ambiguity in decision theory and optimization methods. These methods implement a variety of uncertainty representations from probabilistic and non-probabilistic foundations, including traditional probability theory, sets of probability measures, uncertainty sets, ambiguity sets, possibility theory, evidence theory, fuzzy measures, and imprecise probability. The choice of uncertainty representation impacts the expressiveness and tractability of the decision models. We survey recent approaches for representing uncertainty in both decision making and optimization to clarify the trade-offs among the alternative representations. Robust and distributionally robust optimization are surveyed, with particular attention to standard form ambiguity sets. Applications of uncertainty and decision models are also reviewed, with a focus on recent optimization applications. These applications highlight common practices and potential research gaps. The intersection of behavioral decision making and robust optimization is a promising area for future research and there is also opportunity for further advances in distributionally robust optimization in sequential and multi-agent settings