decision-theory

• Must be acyclic, directed graphs like [[bayesian-network]].

Notation

Node types

• A chance node represents a stochastic variable, noted by circles
• A decision node represents a decision variable, noted by squares
• A utility node represents a [[utility]] variable, noted by diamonds and cannot have children

Edge types

• A conditional edge ends in a chance node, and indicates the uncertainty in the chance node conditioned by its parent values
• An informational edge ends in a decision node, indicating the node was made based on the values of its parents. Usually drawn with dashed lines, or omitted.
• A functional edge is similar to the informational edge, but for utility nodes.

The figure below demonstrates the abstraction, albeit not in a particularly linear way. The utility node represents the joint values of the decision to treat or not, and on the chance we have the disease. The chance of disease is conditioned on the three observables test results.

Concretely, we can solve the decision network by iteratively solving each scenario, and maximizing the utility value $U(T,D)$. The choices/decisions made that maximizes the utility is referred to as a rational decision.

• [[lottery]]
• [[markov-decision-process]]