Vadim, we seem to be talking past each other a bit.
In the linked post, I made some criticisms of some of the (informal/intuitive/motivational) reasoning that was done in the original LI paper. That paper (laudably) makes a number of explicit verbal arguments about why its definitions and results ought to be interesting and promising, and I am disagreeing with those.
In your paper, you are doing something related, but not exactly the same. It’s possible that your paper is different from the original LI paper in a way that answers my criticisms (which would be very interesting to me!). Alternately, it’s possible that my criticisms of the LI paper are not correct to begin with. But these are two different possibilities, and I can’t tell which one you’re addressing here.
The definition of an LI (=something satisfying the LI criterion) in the original paper is based on dominance, and I’ve argued that this is too weak to pick out a category of algorithms with good finite-time properties. Telling me “this thing is an LI,” in the sense used in that paper, tells me nothing about its finite-time properties, for the reasons I explained earlier.
Even granting that, it is of course still possible that some more restrictive criterion, of the form “LI criterion + (something else)”, would pick out a very promising class of algorithms.
So, are you saying
(1) I am wrong and the LI criterion is satisfying (in some way I’m not recognizing)?
(2) I’m right that the LI criterion is unsatisfying, but if we add more specifics, we get something promising? (If so, the “something else” would be very important and I would like to learn more about precisely what it is)
Vadim, we seem to be talking past each other a bit.
In the linked post, I made some criticisms of some of the (informal/intuitive/motivational) reasoning that was done in the original LI paper. That paper (laudably) makes a number of explicit verbal arguments about why its definitions and results ought to be interesting and promising, and I am disagreeing with those.
In your paper, you are doing something related, but not exactly the same. It’s possible that your paper is different from the original LI paper in a way that answers my criticisms (which would be very interesting to me!). Alternately, it’s possible that my criticisms of the LI paper are not correct to begin with. But these are two different possibilities, and I can’t tell which one you’re addressing here.
The definition of an LI (=something satisfying the LI criterion) in the original paper is based on dominance, and I’ve argued that this is too weak to pick out a category of algorithms with good finite-time properties. Telling me “this thing is an LI,” in the sense used in that paper, tells me nothing about its finite-time properties, for the reasons I explained earlier.
Even granting that, it is of course still possible that some more restrictive criterion, of the form “LI criterion + (something else)”, would pick out a very promising class of algorithms.
So, are you saying
(1) I am wrong and the LI criterion is satisfying (in some way I’m not recognizing)?
(2) I’m right that the LI criterion is unsatisfying, but if we add more specifics, we get something promising? (If so, the “something else” would be very important and I would like to learn more about precisely what it is)
(3) Neither of the above?