The fully probabilistic design of dynamic decision strategies is a well-developed theoretical basis for learning decision systems, which are potentially widely applicable in technology, natural and societal systems. Its applicability is constrained by the complexity of the associated optimisation, which is a special version of dynamic programming. In the considered case, it is necessary to approximate a scalar function of many variables, which is implicitly described as a solution of a non-linear integral-difference equation. The solution to this difficult problem can be divided into several PhD theses, which will differ in stress on functional analysis, approximation of functions or various heuristic methods encountered in connection with artificial intelligence. Software or simulation-oriented solutions are welcome.