Computing rank dependent utility in graphical models for sequential decision problems

摘要

This paper is devoted to automated sequential decision in AI. More precisely, we focus here on the Rank Dependent Utility (RDU) model. This model is able to encompass rational decision behaviors that the Expected Utility model cannot accommodate. However, the non-linearity of RDU makes it difficult to compute an RDU-optimal strategy in sequential decision problems. This has considerably slowed the use of RDU in operational contexts. In this paper, we are interested in providing new algorithmic solutions to compute an RDU-optimal strategy in graphical models. Specifically, we present algorithms for solving decision tree models and influence diagram models of sequential decision problems. For decision tree models, we propose a mixed integer programming formulation that is valid for a subclass of RDU models (corresponding to risk seeking behaviors). This formulation reduces to a linear program when mixed strategies are considered. In the general case (i.e., when there is no particular assumption on the parameters of RDU), we propose a branch and bound procedure to compute an RDU-optimal strategy among the pure ones. After highlighting the difficulties induced by the use of RDU in influence diagram models, we show how this latter procedure can be extended to optimize RDU in an influence diagram. Finally, we provide empirical evaluations of all the presented algorithms.