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Solving Stochastic Nonlinear Resource Allocation Problems Using a Hierarchy of Twofold Resource Allocation Automata

机译：使用双重资源分配自动机的层次结构解决随机非线性资源分配问题

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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.
机译：在许多现实情况下，必须根据不完整和嘈杂的信息分配资源。但是，在许多情况下，信息的不完整和嘈杂使传统的资源分配技术无效。最近提出了一种分散式学习自动机背包游戏（LAKG）来解决这类问题，即随机非线性分数阶背包问题。根据经验，与基于传统参数估计方案的方法相比，LAKG具有更好的性能。本文提出了一种全新的在线学习自动机（LA）系统，即双重资源分配自动机的层次结构（H-TRAA）。在贡献方面，我们首先注意到，H-TRAA的原始组件是双向资源分配自动机（TRAA），在LA领域具有新颖性。其次，本文包含对TRAA的形式分析，包括对其收敛性的严格证明。第三，本文证明了H-TRAA本身的收敛性。最后，我们凭经验证明，与LAKG相比，与两种材料单位值函数有关的模拟数据，H-TRAA提供的收敛速度快几个数量级。的确，与LAKG相比，H-TRAA可按比例线性缩放。因此，我们相信H-TRAA为处理要求苛刻的实际应用打开了途径，例如在大规模Web可访问性评估问题中分配采样资源。我们目前正在努力将H-TRAA解决方案应用于适用于万维网的网络轮询和样本大小检测问题。

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