Adam Klivans comments

A few comments:

  1. In general, I don’t think I spent enough time relating my work to other areas of computer science. I think that a fuller comparison to research in say statistical learning theory (as opposed to just computational learning theory) would have emphasized the importance and richness of the topic of learning linear models (e.g., halfspaces). For example, in retrospect, the agnostic learning model actually predates the PAC model (minus the computational considerations) and appears in the work of Vapnik. He referred to the problem of finding the “best fitting” hyperplane as “Empirical Risk Minimization” for hyperplanes. I don’t think the phrase empirical risk minimization appears anywhere in my proposal. Additionally, I just sort of assert that the problem is important, rather than actually giving a bunch of citations [I’m not sure why I did that]. In general, I think it is powerful to cite papers that use/have been directly influenced by either your work or the problem you are working on.
  2. I also don’t think I spent enough time comparing/contrasting my work on learning convex sets with prior geometric approaches of Blum, Kannan, and Vempala. I cite them, but I think it would have been useful for me to think harder about how my work relates to theirs.
  3. Did I need to spend all of that time defining models of learning in the beginning? Maybe I could’ve moved that to an appendix to keep the narrative flow going.
  4. I think my proposal is a bit long. For example, I feel like some of the sections in the “hardness” results could’ve been cut. I wasn’t that exciting about the hardness of proper learning, but I had a decent result in the area, so I felt compelled to mention it.
  5. I still like my use of bulleted, bold-faced questions to emphasize exactly what type of problems I’ll be solving. I find that reviewers often read these things the night before in a hotel room, and it is useful to give them guidance (rather than have them wade through a dense paragraph of text).
  6. Several of my approaches for positive results have been shown, provably, to fail. Bummer. The difficulty of this sort of thing is the usual “if I had a truly promising approach for solving this problem then I would’ve just solved it rather than listing a promising approach” paradox.

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