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On Basing Lower-Bounds for Learning on Worst-Case Assumptions Benny Applebaum
 

Summary: On Basing Lower-Bounds for Learning on Worst-Case Assumptions
Benny Applebaum
Boaz Barak
David Xiao
Abstract
We consider the question of whether P = NP im-
plies that there exists some concept class that is effi-
ciently representable but is still hard to learn in the
PAC model of Valiant (CACM '84), where the learner
is allowed to output any efficient hypothesis approxi-
mating the concept, including an "improper" hypoth-
esis that is not itself in the concept class. We show
that unless the Polynomial Hierarchy collapses, such a
statement cannot be proven via a large class of reduc-
tions including Karp reductions, truth-table reductions,
and a restricted form of non-adaptive Turing reduc-
tions. Also, a proof that uses a Turing reduction of
constant levels of adaptivity would imply an important
consequence in cryptography as it yields a transforma-
tion from any average-case hard problem in NP to a

  

Source: Applebaum, Benny - Faculty of Mathematics and Computer Science, Weizmann Institute of Science

 

Collections: Computer Technologies and Information Sciences