For (3), environments which “almost” have the right symmetries should also “almost” obey the theorems. To give a quick, non-legible sketch of my reasoning:
For the uniform distribution over reward functions on the unit hypercube ([0,1]|S|), optimality probability should be Lipschitz continuous on the available state visit distributions (in some appropriate sense). Then if the theorems are “almost” obeyed, instrumentally convergent actions still should have extremely high probability, and so most of the orbits still have to agree.
So I don’t currently view (3) as a huge deal. I’ll probably talk more about that another time.
That quote does not seem to mention the “stochastic sensitivity issue”. In the post that you linked to, “(3)” refers to:
Not all environments have the right symmetries
But most ones we think about seem to
So I’m still not sure what you meant when you wrote “The phenomena you discuss are explained in the paper (EDIT: top of page 9), and in other posts, and discussed at length in other comment threads.”
(Again, I’m not aware of any previous mention of the “stochastic sensitivity issue” other than in my comment here.)
That quote does not seem to mention the “stochastic sensitivity issue”. In the post that you linked to, “(3)” refers to:
So I’m still not sure what you meant when you wrote “The phenomena you discuss are explained in the paper (EDIT: top of page 9), and in other posts, and discussed at length in other comment threads.”
(Again, I’m not aware of any previous mention of the “stochastic sensitivity issue” other than in my comment here.)