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 constraints

on time and space. One of the advantages of influence diagrams (IDs) is that for small

decision problems, the distinction between phases does not confront the decision maker

with a problem; when the problem has been properly specified, the solution algorithms are

so efficient that the ID can also be used as an on-line representation of the solution. If the

solution algorithm cannot meet the on-line requirements, you will construct an alternative

structure for representing the optimal strategy, for example a look-up table or a strategy

tree. We report on ongoing work with situations where the solution algorithm is too space

and 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 have

separate ID representations for each decision variable. In each representation the actual

information is fully exploited, however the representation of policies for future decisions

are approximations. We call the approximation information abstraction. It consists in

introducing a dummy structure connecting the past with the decision. We study how to

specify, implement and learn information abstraction.