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Team learning as a game

  • Andris Ambainis
  • Kalvis Apsītis
  • Rūsiņš freivalds
  • William Gasarch
  • Carl H. Smith
Session 2
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1316)

Abstract

A machine FIN-learning machine M receives successive values of the function f it is learning; at some point M outputs conjecture which should be a correct index of f. When n machines simultaneously learn the same function f and at least k of these machines outut correct indices of f, we have team learning [k,n]FIN. Papers [DKV92, DK96] show that sometimes a team or a robabilistic learner can simulate another one, if its probability p (or team success ratio k/n) is close enough. On the other hand, there are critical ratios which mae simulation o FIN(p2) by FIN(p1) imossible whenever p2 _< r < p1 or some critical ratio r. Accordingly to [DKV92] the critical ratio closest to 1/2 rom the let is 24/49; [DK96] rovides other unusual constants. These results are comlicated and rovide a ull icture o only or FIN- learners with success ratio above 12/25.

We generalize [k, n]FIN teams to asymmetric teams [AFS97]. We introduce a two player game on two 0-1 matrices defining two asymmetric teams. The result of the game reflects the comparative power of these asymmetric teams. Hereby we show that the problem to determine whether [k1]FIN ⊂ [k2, n2]FIN is algorithmically solvable. We also show that the set of all critical ratios is well-ordered. Simulating asymmetric teams with probabilistic machines from [AFS97] provides some insight about the unusual constants like 24/49.

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Copyright information

© Springer-Verlag Berlin Heidelberg 1997

Authors and Affiliations

  • Andris Ambainis
    • 1
  • Kalvis Apsītis
    • 2
  • Rūsiņš freivalds
    • 1
  • William Gasarch
    • 2
  • Carl H. Smith
    • 2
  1. 1.Institute of Mathematics and Computer ScienceUniversity of LatviaRīgaLatvia
  2. 2.Department of Computer ScienceUniversity of MarylandCollege ParkUSA

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