I’m not sure why we need to say “from E, F, B(), and v, …” instead of just “from E and v”. It seems like B() is just a generic agent design, and the distribution over F can be determined from E, B(), v.
So my restatement of this is something like: “for each R select a distribution f(R), such that if R comes from some prior and v∼f(R), then the mutual information I(R;v)≤k”. v has to not change much dependent on R, so it has to satisfy many different restrictions (about a 1/ek portion?). It seems like this will lead to v satisfying restriction R and also something like a 1/ek portion of the other restrictions in our prior (specifically, the most convenient ones to jointly satisfy).
I’m not sure why we need to say “from E, F, B(), and v, …” instead of just “from E and v”. It seems like B() is just a generic agent design, and the distribution over F can be determined from E, B(), v.
So my restatement of this is something like: “for each R select a distribution f(R), such that if R comes from some prior and v∼f(R), then the mutual information I(R;v)≤k”. v has to not change much dependent on R, so it has to satisfy many different restrictions (about a 1/ek portion?). It seems like this will lead to v satisfying restriction R and also something like a 1/ek portion of the other restrictions in our prior (specifically, the most convenient ones to jointly satisfy).