Direct Data-Driven Methods for Decision Making under Uncertainty

where the future cost f depends both on the decision u ∈ U as well as the outcome of uncertain events, represented by a random variable X ∈ X . Here the random variable X follows a distribution P which is assumed to be known in order to form the expectation in problem (1). Examples includes making an inventory decision with uncertainty future demand, purchasing stocks with uncertain information about the future price, and deciding which PhD programs to choose to go with uncertainty in research directions, advisors and funding opportunities.