Resolute Choice in Sequential Decision Problems with Multiple Priors

This paper is devoted to sequential decision mak-ing under uncertainty, in the multi-prior framework of Gilboa and Schmeidler [1989]. In this setting, a set of probability measures (priors) is defined in-stead of a single one, and the decision maker selects a strategy that maximizes the minimum possible value of expected utility over this set of priors. We are interested here in the resolute choice approach, where one initially commits to a complete strat-egy and never deviates from it later. Given a de-cision tree representation with multiple priors, we study the problem of determining an optimal strat-egy from the root according to min expected utility. We prove the intractability of evaluating a strategy in the general case. We then identify different prop-erties of a decision tree that enable to design dedi-cated resolution procedures. Finally, experimental results are presented that evaluate these procedures.