Monte Carlo methods for exact & efficient solution of the generalized optimality equations

Previous work has shown that classical sequential decision making rules, including expectimax and minimax, are limit cases of a more general class of bounded rational planning problems that trade off the value and the complexity of the solution, as measured by its information divergence from a given reference. This allows modeling a range of novel planning problems having varying degrees of control due to resource constraints, risk-sensitivity, trust and model uncertainty. However, so far it has been unclear in what sense information constraints relate to the complexity of planning. In this paper, we introduce Monte Carlo methods to solve the generalized optimality equations in an efficient & exact way when the inverse temperatures in a generalized decision tree are of the same sign. These methods highlight a fundamental relation between inverse temperatures and the number of Monte Carlo proposals. In particular, it is seen that the number of proposals is essentially independent of the size of the decision tree.