Online non-convex learning for river pollution source identification

TL;DR

This paper introduces novel online gradient-based algorithms for real-time river pollution source identification, effectively estimating pollution parameters with high accuracy and theoretical guarantees, outperforming existing methods in practical scenarios.

Contribution

The paper develops adaptive, vectorized online algorithms with saddle point escape mechanisms for non-convex pollution source estimation, providing theoretical regret bounds and practical validation.

Findings

Algorithms achieve $O(N)$ local regret and high probability $O(N)$ cumulative regret.

Real-life case study demonstrates superior estimation accuracy.

The methods outperform existing approaches in accuracy and robustness.

Abstract

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.