Preference elicitation in Fully Probabilistic Design of decision strategies

Abstract

Any systematic decision-making design selects a decision strategy that makes the resulting closed-loop behaviour close to the desired one. Fully Probabilistic Design (FPD) describes modelled and desired closed-loop behaviours via their distributions. The designed strategy is a minimiser of Kullback-Leibler divergence of these distributions. FPD: i) unifies modelling and aim-expressing languages; ii) directly describes multiple aims and constraints; iii) simplifies an (inevitable) approximate design as it has an explicit minimiser. The paper enriches the theory of FPD, in particular, it: i) improves its axiomatic basis; ii) quantitatively relates FPD to standard Bayesian decision making showing that the set of FPD tasks is a dense extension of Bayesian problem formulations; iii) opens a way to a systematic data-based preference elicitation, i.e., quantitative expression of decision-making aims.