See Judea Pearl’s Probablilistic Reasoning in Intelligent Systems, section 7.3, for a discussion of “metaprobabilities” in the context of graphical models.
Although it’s true that you could compute the correct decision by directly putting a distribution on all possible futures, the computational complexity of this strategy grows combinatorially as the scenario gets longer. This isn’t a minor point; generalizing the brute force method gets you AIXI. That is why you need something like the A_p distribution or Pearl’s “contingencies” to store evidence and reason efficiently.
See Judea Pearl’s Probablilistic Reasoning in Intelligent Systems, section 7.3, for a discussion of “metaprobabilities” in the context of graphical models.
Although it’s true that you could compute the correct decision by directly putting a distribution on all possible futures, the computational complexity of this strategy grows combinatorially as the scenario gets longer. This isn’t a minor point; generalizing the brute force method gets you AIXI. That is why you need something like the A_p distribution or Pearl’s “contingencies” to store evidence and reason efficiently.