I can readily define asymptotic optimality but I find the notion of Bayes optimality harder to pin down. What is a correct and general mathematical definition of Bayes Optimality?
Note: The notion of asymptotic optimality I have in mind is that in the limit of an infinite amount of data the statistical system converges to the optimal decision. Deep Q-learning is an example of such a method. By Bayes-Optimal my intuition is that it must mean that our system always makes the optimal decision given the available information.