I think this means “indifference” isn’t really the right term any more, because the agent is not actually indifferent between the two sets of observations, and doesn’t really need to be.
So, how about
U(a1, o, a2) = UN(a1, o, a2) + max_b(US(a1, o, b)), if o is not in Press US(a1, o, a2) + max_b(UN(a1, o, b)), if o is in Press
or, in your notation,
U(a1, o, a2) = g(a1, o) + UN(a1, o, a2) if o is in Press, or US(a1, o, a2) + f(a1, o) if o is in Press.
I think this means “indifference” isn’t really the right term any more, because the agent is not actually indifferent between the two sets of observations, and doesn’t really need to be.
So, how about U(a1, o, a2) =
UN(a1, o, a2) + max_b(US(a1, o, b)), if o is not in Press
US(a1, o, a2) + max_b(UN(a1, o, b)), if o is in Press
or, in your notation, U(a1, o, a2) = g(a1, o) + UN(a1, o, a2) if o is in Press, or US(a1, o, a2) + f(a1, o) if o is in Press.