论文标题
部分可观测时空混沌系统的无模型预测
Edge-weighted Online Stochastic Matching: Beating $1-\frac1e$
论文作者
论文摘要
储层计算是预测湍流的有力工具，其简单的架构具有处理大型系统的计算效率。然而，其实现通常需要完整的状态向量测量和系统非线性知识。我们使用非线性投影函数将系统测量扩展到高维空间，然后将其输入到储层中以获得预测。我们展示了这种储层计算网络在时空混沌系统上的应用，该系统模拟了湍流的若干特征。我们表明，使用径向基函数作为非线性投影器，即使只有部分观测并且不知道控制方程，也能稳健地捕捉复杂的系统非线性。最后，我们表明，当测量稀疏、不完整且带有噪声，甚至控制方程变得不准确时，我们的网络仍然可以产生相当准确的预测，从而为实际湍流系统的无模型预测铺平了道路。
We study the edge-weighted online stochastic matching problem. Since Feldman, Mehta, Mirrokni, and Muthukrishnan proposed the $(1-\frac1e)$-competitive Suggested Matching algorithm, there has been no improvement for the general edge-weighted online stochastic matching problem. In this paper, we introduce the first algorithm beating the $1-\frac1e$ barrier in this setting, achieving a competitive ratio of $0.645$. Under the LP proposed by Jaillet and Lu, we design an algorithmic preprocessing, dividing all edges into two classes. Then based on the Suggested Matching algorithm, we adjust the matching strategy to improve the performance on one class in the early stage and on another class in the late stage, while keeping the matching events of different edges highly independent. By balancing them, we finally guarantee the matched probability of every single edge.
