Here’s a different way of framing it: if we don’t make this assumption, is there some useful generalization of UDT which emerges? Or, having not made this assumption, are we stuck in a quagmire where we can’t really say anything useful?
I think about these sorts of ‘technical assumptions’ needed for nice DT results as “sanity checks”:
I think we need to make several significant assumptions like this in order to get nice theoretical DT results.
These nice DT results won’t precisely apply to the real world; however, they do show that the DT being analyzed at least behaves sanely when it is in these ‘easier’ cases.
So it seems like the natural thing to do is prove tiling results, learning results, etc under the necessary technical assumptions, with some concern for how restrictive the assumptions are (broader sanity checks being better), and then also, check whether behavior is “at least somewhat reasonable” in other cases.
So if UDT fails to tile when we remove these assumptions, but, at least appears to choose its successor in a reasonable way given the situation, this would count as a success.
Better, of course, if we can find the more general DT which tiles under weaker assumptions. I do think it’s quite plausible that UDT needs to be generalized; I just expect my generalization of UDT will still need to make an assumption which rules out your counterexample to UDT.
Here’s a different way of framing it: if we don’t make this assumption, is there some useful generalization of UDT which emerges? Or, having not made this assumption, are we stuck in a quagmire where we can’t really say anything useful?
I think about these sorts of ‘technical assumptions’ needed for nice DT results as “sanity checks”:
I think we need to make several significant assumptions like this in order to get nice theoretical DT results.
These nice DT results won’t precisely apply to the real world; however, they do show that the DT being analyzed at least behaves sanely when it is in these ‘easier’ cases.
So it seems like the natural thing to do is prove tiling results, learning results, etc under the necessary technical assumptions, with some concern for how restrictive the assumptions are (broader sanity checks being better), and then also, check whether behavior is “at least somewhat reasonable” in other cases.
So if UDT fails to tile when we remove these assumptions, but, at least appears to choose its successor in a reasonable way given the situation, this would count as a success.
Better, of course, if we can find the more general DT which tiles under weaker assumptions. I do think it’s quite plausible that UDT needs to be generalized; I just expect my generalization of UDT will still need to make an assumption which rules out your counterexample to UDT.