9.5.1 Utility Theory and Rationality

This section provides some justification for using cost functions and then minimizing their expected value under Formulations 9.3 and 9.4. The resulting framework is called utility theory, which is usually formulated using rewards instead of costs. As stated in Section 9.1.1, a cost can be converted into a reward by multiplying by $-1$ and then swapping each maximization with minimization. We will therefore talk about a reward $R$ with the intuition that a higher reward is better.