Approximate representation of optimal strategies from influence diagrams

There are three phases in the life of a decision problem, specification, solution, and rep-resentation of solution. The specification and solution phases are off-line, while the rep-resention of solution often shall serve an on-line situation with rather tough constraintson time and space. One of the advantages of influence diagrams (IDs) is that for smalldecision problems, the distinction between phases does not confront the decision makerwith a problem; when the problem has been properly specified, the solution algorithms areso efficient that the ID can also be used as an on-line representation of the solution. If thesolution algorithm cannot meet the on-line requirements, you will construct an alternativestructure for representing the optimal strategy, for example a look-up table or a strategytree. We report on ongoing work with situations where the solution algorithm is too spaceand time consuming, and where the policy functions for the decisions have so large do-mains that they cannot be represented directly in a strategy tree. The approach is to haveseparate ID representations for each decision variable. In each representation the actualinformation is fully exploited, however the representation of policies for future decisionsare approximations. We call the approximation information abstraction. It consists inintroducing a dummy structure connecting the past with the decision. We study how tospecify, implement and learn information abstraction.