The Complexity of Learning According to Two Models of a Drifting Environment

  • Authors:
  • Philip M. Long

  • Affiliations:
  • Department of Computer Science, National University of Singapore, Singapore 119260, Republic of Singapore. plong@comp.nus.edu.sg

  • Venue:
  • Machine Learning - The Eleventh Annual Conference on computational Learning Theory
  • Year:
  • 1999

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Abstract

We show that a \frac{c \epsilon^3}{VC dim({\cal F})}bound on the rate of drift of the distribution generating theexamples is sufficient for agnostic learning to relative accuracyε, where c 0 is a constant; this matches aknown necessary condition to within a constant factor. We establisha \frac{c\epsilon^2}{VC dim({\cal F})} sufficient conditionfor the realizable case, also matching a known necessary condition towithin a constant factor. We provide a relatively simple proof of abound of O(\frac{1}{\epsilon^2} (VC dim({\cal F}) +log \frac{1}{\delta})) on the sample complexity of agnosticlearning in a fixed environment.