Recap of L09: Normative Decision Theory Page 1 Recap of L09: Normative Decision Theory

Decision Tree for Oil Wildcatter Page 2 Decision Tree for Oil Wildcatter Classical way to represent decision problems with multiple decisions Explicitly show all possible sequences of decisions and observations. Example: Oil Wildcatter

Solving Decision Trees Page 3 Solving Decision Trees

Solving Decision Trees Page 4 Solving Decision Trees

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Influence Diagram A DAG with three types of nodes Chance nodes, decision nodes, and utility nodes There is a directed path containing all the decision nodes. The utility nodes have no children. Each chance node is associated with the conditional distribution given its parents. Each utility node is associated with a utility function, a real-valued function of its parents.

Influence Diagram An influence diagram for the oil wildcatter problem Page 7 Influence Diagram An influence diagram for the oil wildcatter problem Decision: T: test = {y, n}; D: drill={y, n} Utility: C: cost of test ; V: Benefit of drilling Chance: O: Oil ={dry, wet, soaking} R: seismic structure {no-structure, open-structure, closed-structure, no-result}

Finding Optimal Policy Page 8 Finding Optimal Policy First idea: Convert to decision tree and solve it Exponential still! Next: Variable Elimination Algorithm for solving influence diagrams Note BN inference: All orderings give correct result, but might have different complexity ID: Must use “strong elimination orderings”.