A framework for sensitivity analysis of decision trees

Bogumił Kamiński, Michał Jakubczyk, Przemysław Szufel

In the paper, we consider sequential decision problems with uncertainty, represented as decision trees. Sensitivity analysis is always a crucial element of decision making and in decision trees it often focuses on probabilities. In the stochastic model considered, the user often has only limited information about the true values of probabilities. We develop a framework for performing sensitivity analysis of optimal strategies accounting for this distributional uncertainty. We design this robust optimization approach in an intuitive and not overly technical way, to make it simple to apply in daily managerial practice. The proposed framework allows for (1) analysis of the stability of the expected-value-maximizing strategy and (2) identification of strategies which are robust with respect to pessimistic/optimistic/mode-favoring perturbations of probabilities. We verify the properties of our approach in two cases: (a) probabilities in a tree are the primitives of the model and can be modified independently; (b) probabilities in a tree reflect some underlying, structural probabilities, and are interrelated. We provide a free software tool implementing the methods described.