Fully probabilistic design unifies and supports dynamic decision making under uncertainty

Abstract

The fully probabilistic design (FPD) of decision strategies models the closed decision loop as well as decision aims and constraints by joint probabilities of involved variables. FPD takes the minimiser of cross entropy (CE) of the closed-loop model to its ideal counterpart, expressing the decision aims and constraints, as the optimal strategy. FPD: (a) got an axiomatic basis; (b) extended the decision making (DM) optimising a subjective expected utility (SEU); (c) was nontrivially applied; (d) advocated CE as a proper similarity measure for an approximation of a given probability distribution; (d) generalised the minimum CE principle for a choice of the distribution, which respects its incomplete specification; (e) has opened a way to the cooperation based on sharing of probability distributions. When trying to survey the listed results, scattered in a range of publications, we have found that the results under (b), (d) and (e) can be refined and non-trivially generalised. This determines the paper aims: to provide a complete concise description of FPD with its use and open problems outlined.