Lecture Notes Link Uncertainty Representation to Optimal Decision Making

A new lecture note on arXiv (2607.14407v3) explores the critical role of uncertainty quantification in decision-making systems. The authors argue that many signal processing systems are designed to act, and the way uncertainty is represented directly impacts performance and trustworthiness. The note develops, from first principles, a decision-theoretic framework linking an agent's objective and knowledge to the form of uncertainty representation sufficient for optimal action. For known environments, a risk-neutral agent requires the posterior distribution over the state, while a risk-averse agent can rely on a prediction set and a worst-case decision rule without loss of optimality. For unknown environments, the note identifies three complementary approaches to address epistemic uncertainty. The work is relevant to artificial intelligence, machine learning, and control systems, where reliable decision-making under uncertainty is paramount. The lecture note is available at https://arxiv.org/abs/2607.14407.