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Triadic-OCD: Asynchronous Online Change Detection with Provable Robustness, Optimality, and Convergence

Yancheng Huang, Kai Yang, Zelin Zhu, Leian Chen

TL;DR

Triadic-OCD tackles online change detection under uncertain system parameters by formulating a nested, asynchronous distributed optimization problem. It combines cutting-plane methods with an augmented-Lagrangian and inner gradient steps to estimate uncertain system components, and proves non-asymptotic convergence to an $ε$-optimal point. The approach yields provable robustness to parameter uncertainty and optimality under certain conditions, while reducing communication and straggler effects through asynchronous updates. Empirical results on the IEEE 14-bus smart grid benchmark demonstrate faster detection and greater resilience to uncertainty than state-of-the-art baselines, highlighting practical benefits for FDIA detection in distributed settings.

Abstract

The primary goal of online change detection (OCD) is to promptly identify changes in the data stream. OCD problem find a wide variety of applications in diverse areas, e.g., security detection in smart grids and intrusion detection in communication networks. Prior research usually assumes precise knowledge of the system parameters. Nevertheless, this presumption often proves unattainable in practical scenarios due to factors such as estimation errors, system updates, etc. This paper aims to take the first attempt to develop a triadic-OCD framework with certifiable robustness, provable optimality, and guaranteed convergence. In addition, the proposed triadic-OCD algorithm can be realized in a fully asynchronous distributed manner, easing the necessity of transmitting the data to a single server. This asynchronous mechanism could also mitigate the straggler issue that faced by traditional synchronous algorithm. Moreover, the non-asymptotic convergence property of Triadic-OCD is theoretically analyzed, and its iteration complexity to achieve an $ε$-optimal point is derived. Extensive experiments have been conducted to elucidate the effectiveness of the proposed method.

Triadic-OCD: Asynchronous Online Change Detection with Provable Robustness, Optimality, and Convergence

TL;DR

Triadic-OCD tackles online change detection under uncertain system parameters by formulating a nested, asynchronous distributed optimization problem. It combines cutting-plane methods with an augmented-Lagrangian and inner gradient steps to estimate uncertain system components, and proves non-asymptotic convergence to an -optimal point. The approach yields provable robustness to parameter uncertainty and optimality under certain conditions, while reducing communication and straggler effects through asynchronous updates. Empirical results on the IEEE 14-bus smart grid benchmark demonstrate faster detection and greater resilience to uncertainty than state-of-the-art baselines, highlighting practical benefits for FDIA detection in distributed settings.

Abstract

The primary goal of online change detection (OCD) is to promptly identify changes in the data stream. OCD problem find a wide variety of applications in diverse areas, e.g., security detection in smart grids and intrusion detection in communication networks. Prior research usually assumes precise knowledge of the system parameters. Nevertheless, this presumption often proves unattainable in practical scenarios due to factors such as estimation errors, system updates, etc. This paper aims to take the first attempt to develop a triadic-OCD framework with certifiable robustness, provable optimality, and guaranteed convergence. In addition, the proposed triadic-OCD algorithm can be realized in a fully asynchronous distributed manner, easing the necessity of transmitting the data to a single server. This asynchronous mechanism could also mitigate the straggler issue that faced by traditional synchronous algorithm. Moreover, the non-asymptotic convergence property of Triadic-OCD is theoretically analyzed, and its iteration complexity to achieve an -optimal point is derived. Extensive experiments have been conducted to elucidate the effectiveness of the proposed method.
Paper Structure (14 sections, 5 theorems, 126 equations, 4 figures, 1 algorithm)

This paper contains 14 sections, 5 theorems, 126 equations, 4 figures, 1 algorithm.

Table of Contents

  1. Introduction
  2. Related Work
  3. Problem Statement
  4. Nested Optimization
  5. Asynchronous Distributed Method
  6. Theoretical Analysis
  7. Experiment
  8. Dateset
  9. Numerical Results
  10. Conclusion
  11. Experimental Settings
  12. Derivation of (\ref{['v_t']})
  13. Complete Proof of Theorem \ref{['theorem_2']}
  14. Proof of Theorem \ref{['theorem_1']}

Key Result

Theorem 6.1

As the set of cutting planes is continuously updated, the optimal objective value of the approximation problem (distributed_3) converges monotonically.

Figures (4)

  • Figure 1: Performance comparison of different detection algorithms.
  • Figure 2: Performance of Triadic-OCD under various uncertainty Sets.
  • Figure 3: Successful detection rate versus the corresponding upper bound on detection delay.
  • Figure 4: Convergence speed comparison between Triadic-OCD and its synchronous counterpart.

Theorems & Definitions (13)

  • Theorem 6.1
  • Definition 6.2
  • Theorem 6.4
  • Definition 3.1
  • Definition 3.2
  • Definition 3.3
  • Lemma 3.4
  • proof
  • Lemma 3.5
  • proof
  • ...and 3 more