[JLJ An Influence Diagram is an excellent theoretical
concept to use as one component of an evaluation function for a computer playing a game. It needs to be matched with an effective
strategy for focusing the machine's efforts on the moves that are promising, interesting, risk mitigating and resilient in
the face of unknown, future threats.]
p.1 This paper will look at the development of in
fluence diagrams from their beginnings in decision analysis to their
current important place in many areas of computer science including artificial intelligence. We will layout the different
methods used to optimize decisions using influence diagrams by computing them directly or via conversions to other models
such as decision graphs and bayesian networks. The latter type in particular will be looked at in depth and it will be contrasted
against the performance of various algorithms.
p.1 In
fluence diagrams (IDs) were proposed by Howard and Matheson [HM03] as a tool to simplify modelling and analysis
of decision trees. Decision trees represent each decision or chance variable as a new level in a tree. The leaves
of the tree are utilities that express which ending configurations are more desirable. Solving a decision problem requires
finding the optimal path through this tree that maximizes expected utility.
p.3 IDs [Influence Diagrams] have several known advantages over decision trees. They simplify
modelling by allowing the analyst to specify single nodes that represent entire probability distributions over nearly arbitrary
relationships with other variables. We still limit ourselves to regularity as defined above and no loops but this
still provides a level of expression not possible with trees... influence diagrams have much to offer if they can be evaluated
efficiently.
p.3 Cooper [Coo88] converted the ID problem to a BN [Bayesian
Network] problem in the following way. An influence diagram is essentially very similar to a bayesian network already,
all that is required is to ensure that all nodes have proper probability distributions associated
with them to allow us to perform inference.
