Table 1 of the paper (pg. 3) is a very nice visual of the different settings.
For the “Theorem: Training retargetability criterion”, where f(A, u) >= its involution, what would be the case where it’s not greater/equal to it’s involution? Is this when the options in B are originally more optimal?
Also, that theorem requires each involution to be greater/equal than the original. Is this just to get a lower bound on the n-multiple or do less-than involutions not add anything?
For the “Theorem: Training retargetability criterion”, where f(A, u) >= its involution, what would be the case where it’s not greater/equal to it’s involution? Is this when the options in B are originally more optimal?
I don’t think I understand the question. Can you rephrase?
Also, that theorem requires each involution to be greater/equal than the original. Is this just to get a lower bound on the n-multiple or do less-than involutions not add anything?
Less-than involutions aren’t guaranteed to add anything. For example, if f(a)=1 iff a goes left and 0 otherwise, any involutions to plans going right will be 0, and all orbits will unanimously agree that left is greater f-value.
Table 1 of the paper (pg. 3) is a very nice visual of the different settings.
For the “Theorem: Training retargetability criterion”, where f(A, u) >= its involution, what would be the case where it’s not greater/equal to it’s involution? Is this when the options in B are originally more optimal?
Also, that theorem requires each involution to be greater/equal than the original. Is this just to get a lower bound on the n-multiple or do less-than involutions not add anything?
I don’t think I understand the question. Can you rephrase?
Less-than involutions aren’t guaranteed to add anything. For example, if f(a)=1 iff a goes left and 0 otherwise, any involutions to plans going right will be 0, and all orbits will unanimously agree that left is greater f-value.
Your example actually cleared this up for me as well! I wanted an example where the inequality failed even if you had an involution on hand.