The weak aggregating algorithm and weak mixability

  • Authors:
  • Yuri Kalnishkan;Michael V. Vyugin

  • Affiliations:
  • Department of Computer Science and Computer Learning Research Centre, Royal Holloway, University of London, Egham, Surrey, TW20 0EX, United Kingdom;Department of Computer Science and Computer Learning Research Centre, Royal Holloway, University of London, Egham, Surrey, TW20 0EX, United Kingdom

  • Venue:
  • Journal of Computer and System Sciences
  • Year:
  • 2008

Quantified Score

Hi-index 0.00

Visualization

Abstract

This paper resolves the problem of predicting as well as the best expert up to an additive term of the order o(n), where n is the length of a sequence of letters from a finite alphabet. We call the games that permit this weakly mixable and give a geometrical characterisation of the class of weakly mixable games. Weak mixability turns out to be equivalent to convexity of the finite part of the set of superpredictions. For bounded games we introduce the Weak Aggregating Algorithm that allows us to obtain additive terms of the form Cn.