Week 10 - Decision Making

What is a utility function?

A function U(s) that assigns a numerical value to each state, representing the agent’s preference.

What is the principle of Maximum Expected Utility (MEU)?

The rational agent chooses the action a* that maximizes expected utility: EU(a) = ∑ P(s|a) × U(s).

What makes an agent's preferences rational?

They must be complete and transitive, and satisfy continuity, substitutability, monotonicity, and decomposability.

What are the components of a decision network?

Chance nodes (ovals), decision nodes (rectangles), and utility nodes (diamonds).

How do you compute expected utility in a decision network?

EU(action) = ∑ P(outcome | action) × U(outcome), summing over possible outcomes.

What is the 'rollback method' in decision networks?

Unroll the network into a tree, compute utility at leaves, work backward to find expected utility and optimal decisions.

How does human behavior deviate from utility theory?

Humans often exhibit risk aversion or risk-seeking behaviors, especially with money or high-stakes outcomes.

What is a lottery in decision theory?

A probabilistic combination of outcomes, e.g., [p, A; (1−p), B], used to analyze preferences under uncertainty.

What is the Value of Perfect Information (VPI)?

The increase in expected utility from making a decision with additional evidence vs. without it.

When is information valuable in decision-making?

When it is likely to change the decision and the stakes are high.

What is the formula for VPI?

VPI(e) = EU(with evidence e) − EU(without evidence). It is always non-negative.

What example illustrates decision theory with uncertainty?

The umbrella problem: choosing whether to bring an umbrella based on forecast or prior probabilities.

What is the impact of high-stakes decisions on information value?

Even small changes in utility may justify obtaining information if the consequences are significant (e.g., death).