Lazy Fully Probabilistic Design of Decision Strategies

Fully probabilistic design of decision strategies (FPD) extends Bayesian dynamic decision making. The FPD specifies the decision aim via so-called ideal - a probability density, which assigns high probability values to the desirable behaviours and low values to undesirable ones. The optimal decision strategy minimises the Kullback-Leibler divergence of the probability density describing the closed-loop behaviour to this ideal. In spite of the availability of explicit minimisers in the corresponding dynamic programming, it suffers from the curse of dimensionality connected with complexity of the value function. Recently proposed a lazy FPD tailors lazy learning, which builds a local model around the current behaviour, to estimation of the closed-loop model with the optimal strategy. This paper adds a theoretical support to the lazy FPD and outlines its further improvement.