Decision Making Needs Uncertainty Quantification [Lecture Notes]

תקציר מקורי באנגליתarXiv:2607.14407v4 Announce Type: replace-cross Abstract: Many signal processing systems ultimately exist to act. Whenever the state variable that determines the action to be taken by a decision maker, or agent, is uncertain, the way that uncertainty is represented decides how well the agent performs and how much its performance can be trusted. This lecture note develops, from first principles and within a single decision-theoretic setting, the link between the {objective} and the knowledge of an agent and the form of uncertainty representation that is sufficient to act optimally. To start, assuming a known environment distribution, we show that a risk-neutral agent needs the posterior distribution over the state, whereas a risk-averse agent can rely without loss of optimality on a {predic