论文标题

用于河流污染源识别的在线非凸学习

Online non-convex learning for river pollution source identification

论文作者

Huang, Wenjie, Jiang, Jing, Liu, Xiao

论文摘要

在本文中,开发了基于梯度的新型在线学习算法来研究重要的环境应用:实时河流污染源识别,旨在估算基于下游传感器数据监测污染浓度的河流污染源的释放质量,位置和时间。假定污染是瞬时释放的。该问题可以作为统计学习中的非convex损失最小化问题提出,并且我们的在线算法已经对矢量化和自适应步骤尺寸进行了矢量化和自适应阶跃尺寸,以确保在具有不同幅度不同的三个维度的高估计准确性。为了防止算法陷入非凸损失的鞍点,从鞍点模块和多启动设置中逃脱的设置被得出以进一步提高估计准确性,以搜索损失函数的全局最小化器。这可以在理论上和实验上显示为算法的本地遗憾,以及在特定的损失功能中的特定错误绑定条件下,$ o(n)$的高概率累积遗憾。现实生活中的河流污染源识别示例显示,就估计精度而言,与现有方法相比,我们算法的出色性能。还提供了为决策者使用算法的管理洞察力。

In this paper, novel gradient-based online learning algorithms are developed to investigate an important environmental application: real-time river pollution source identification, which aims at estimating the released mass, location, and time of a river pollution source based on downstream sensor data monitoring the pollution concentration. The pollution is assumed to be instantaneously released once. The problem can be formulated as a non-convex loss minimization problem in statistical learning, and our online algorithms have vectorized and adaptive step sizes to ensure high estimation accuracy in three dimensions which have different magnitudes. In order to keep the algorithm from stucking to the saddle points of non-convex loss, the escaping from saddle points module and multi-start setting are derived to further improve the estimation accuracy by searching for the global minimizer of the loss functions. This can be shown theoretically and experimentally as the $O(N)$ local regret of the algorithms and the high probability cumulative regret bound $O(N)$ under a particular error bound condition in loss functions. A real-life river pollution source identification example shows the superior performance of our algorithms compared to existing methods in terms of estimation accuracy. Managerial insights for the decision maker to use the algorithms are also provided.

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