Problem

Consider the problem of computing the optimal action for an agent whose utility function we are uncertain about. In particular, assume that, rather than a known utility function over outcomes O, we have a probability density function P(U), which assigns a density for each possible utility function U: O → IR.

a. What is the expected utility for a given action a, taking an expectation both over the outcomes of πa, and over the possible utility functions that the agent might have?

b. Use your answer to provide an efficient computation of the optimal action for the agent.