A Hierarchy of Twofold Resource Allocation Automata Supporting Optimal Sampling

  • Authors:
  • Ole-Christoffer Granmo;B. John Oommen

  • Affiliations:
  • Dept. of ICT, University of Agder, Grimstad, Norway;School of Computer Science, Carleton University, Ottawa, Canada

  • Venue:
  • IEA/AIE '09 Proceedings of the 22nd International Conference on Industrial, Engineering and Other Applications of Applied Intelligent Systems: Next-Generation Applied Intelligence
  • Year:
  • 2009

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Abstract

We consider the problem of allocating limited sampling resources in a "real-time" manner with the purpose of estimating multiple binomial proportions. More specifically, the user is presented with `n ' sets of data points, S 1 , S 2 , ..., S n , where the set S i has N i points drawn from two classes {*** 1 , *** 2 }. A random sample in set S i belongs to *** 1 with probability u i and to *** 2 with probability 1 *** u i , with {u i }. i = 1, 2, ...n , being the quantities to be learnt. The problem is both interesting and non-trivial because while both n and each N i are large, the number of samples that can be drawn is bounded by a constant, c . We solve the problem by first modelling it as a Stochastic Non-linear Fractional Knapsack Problem . We then present a completely new on-line Learning Automata (LA) system, namely, the Hierarchy of Twofold Resource Allocation Automata (H-TRAA), whose primitive component is a Twofold Resource Allocation Automaton (TRAA), both of which are asymptotically optimal. Furthermore, we demonstrate empirically that the H-TRAA provides orders of magnitude faster convergence compared to the LAKG which represents the state-of-the-art. Finally, in contrast to the LAKG, the H-TRAA scales sub-linearly. Based on these results, we believe that the H-TRAA has also tremendous potential to handle demanding real-world applications.