A hierarchy of twofold resource allocation automata supporting optimal sampling

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 {ω 1, ω 2}. A random sample in set S i belongs to ω 1 with probability u i and to ω 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. © 2009 Springer Berlin Heidelberg.