Aumann agreement can fail for purely epistemic reasons because real-world minds do not do Bayesian updating. Bayesian updating is intractable so realistic minds sample from the prior. This is how e.g. gradient descent works and also how human minds work.
In this situation a two minds can end in two different basins with similar loss on the data. Because of computational limitations.
These minds can have genuinely different expectation for generalization.
(Of course this does not contradict the statement of the theorem which is correct.)
Trivial but important
Aumann agreement can fail for purely epistemic reasons because real-world minds do not do Bayesian updating. Bayesian updating is intractable so realistic minds sample from the prior. This is how e.g. gradient descent works and also how human minds work.
In this situation a two minds can end in two different basins with similar loss on the data. Because of computational limitations. These minds can have genuinely different expectation for generalization.
(Of course this does not contradict the statement of the theorem which is correct.)