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This paper explores the critical relationship between uncertainty representation and decision-making performance in agents operating under uncertain conditions. It establishes that a risk-neutral agent requires a posterior distribution over the state for optimal action, while a risk-averse agent can achieve the same with a prediction set and a worst-case decision rule. Additionally, it identifies three strategies for managing epistemic uncertainty in unknown environments: calibration of predictors, credal sets with distributionally robust optimization, and Bayesian inference, emphasizing that effective decision-making hinges on aligning uncertainty representation with the agent's knowledge and objectives.
Reliable decision-making hinges on how uncertainty is represented, revealing that risk-averse agents can perform optimally with simpler models than previously thought.
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 {prediction set} and a worst-case decision rule. We then turn to the case in which the environment is unknown, and identify three complementary approaches to address the resulting epistemic uncertainty: calibration of a fixed predictor, credal (ambiguity) sets with distributionally robust optimization, and Bayesian inference over model parameters. The common thread is that reliable decisions require an uncertainty representation matched to the decision objective and to the knowledge profile of the agent, together with a guarantee that certifies the utility the agent will actually obtain.