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This paper considers the nonlinear fractional knapsack problem and demonstrates how its solution can be effectively applied to two resource allocation problems dealing with the World Wide Web. The novel solution involves a "team" of deterministic learning automata (LA). The first real-life problem relates to resource allocation in web monitoring so as to "optimize" information discovery when the polling capacity is constrained. The disadvantages of the currently reported solutions are explained in this paper. The second problem concerns allocating limited sampling resources in a "real-time" manner with the purpose of estimating multiple binomial proportions. This is the scenario encountered when the user has to evaluate multiple web sites by accessing a limited number of web pages, and the proportions of interest are the fraction of each web site that is successfully validated by an HTML validator. Using the general LA paradigm to tackle both of the real-life problems, the proposed scheme improves a current solution in an online manner through a series of informed guesses that move toward the optimal solution. At the heart of the scheme, a team of deterministic LA performs a controlled random walk on a discretized solution space. Comprehensive experimental results demonstrate that the discretization resolution determines the precision of the scheme, and that for a given precision, the current solution (to both problems) is consistently improved until a nearly optimal solution is found--even for switching environments. Thus, the scheme, while being novel to the entire field of LA, also efficiently handles a class of resource allocation problems previously not addressed in the literature.

Purpose -The two-armed Bernoulli bandit (TABB) problem is a classical optimization problem where an agent sequentially pulls one of two arms attached to a gambling machine, with each pull resulting either in a reward or a penalty. The reward probabilities of each arm are unknown, and thus one must balance between exploiting existing knowledge about the arms, and obtaining new information. The purpose of this paper is to report research into a completely new family of solution schemes for the TABB problem: the Bayesian learning automaton (BLA) family. Design/methodology/approach -Although computationally intractable in many cases, Bayesian methods provide a standard for optimal decision making. BLA avoids the problem of computational intractability by not explicitly performing the Bayesian computations. Rather, it is based upon merely counting rewards/penalties, combined with random sampling from a pair of twin Beta distributions. This is intuitively appealing since the Bayesian conjugate prior for a binomial parameter is the Beta distribution. Findings -BLA is to be proven instantaneously self-correcting, and it converges to only pulling the optimal arm with probability as close to unity as desired. Extensive experiments demonstrate that the BLA does not rely on external learning speed/accuracy control. It also outperforms established non-Bayesian top performers for the TABB problem. Finally, the BLA provides superior performance in a distributed application, namely, the Goore game (GG). Originality/value -The value of this paper is threefold. First of all, the reported BLA takes advantage of the Bayesian perspective for tackling TABBs, yet avoids the computational complexity inherent in Bayesian approaches. Second, the improved performance offered by the BLA opens up for increased accuracy in a number of TABB-related applications, such as the GG. Third, the reported results form the basis for a new avenue of research -even for cases when the reward/penalty distribution is not Bernoulli distributed. Indeed, the paper advocates the use of a Bayesian methodology, used in conjunction with the corresponding appropriate conjugate prior.

Abstract-In a multitude of real-world situations, resources must be allocated based on incomplete and noisy information. However, in many cases, incomplete and noisy information render traditional resource allocation techniques ineffective. The decentralized Learning Automata Knapsack Game (LAKG) was recently proposed for solving one such class of problems, namely the class of Stochastic Nonlinear Fractional Knapsack Problems. Empirically, the LAKG was shown to yield a superior performance when compared to methods which are based on traditional parameter estimation schemes. This paper presents a completely new online Learning Automata (LA) system, namely the Hierarchy of Twofold Resource Allocation Automata (H-TRAA). In terms of contributions, we first of all, note that the primitive component of the H-TRAA is a Twofold Resource Allocation Automaton (TRAA) which possesses novelty in the field of LA. Second, the paper contains a formal analysis of the TRAA, including a rigorous proof for its convergence. Third, the paper proves the convergence of the H-TRAA itself. Finally, we demonstrate empirically that the H-TRAA provides orders of magnitude faster convergence compared to the LAKG for simulated data pertaining to two-material unit-value functions. Indeed, in contrast to the LAKG, the H-TRAA scales sublinearly. Consequently, we believe that the H-TRAA opens avenues for handling demanding real-world applications such as the allocation of sampling resources in large-scale web accessibility assessment problems. We are currently working on applying the H-TRAA solution to the web-polling and sample-size detection problems applicable to the world wide web.

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