Is Stochastic Mirror Descent Vulnerable to Adversarial Delay Attacks? A Traffic Assignment Resilience Study

TL;DR

This paper investigates the resilience of intelligent navigation systems using stochastic mirror descent against delay attacks, showing that their performance degrades only mildly under bounded delays, ensuring stability in traffic assignment.

Contribution

It introduces a theoretical analysis of INS robustness under delay attacks using the Wardrop Non-Equilibrium Solution framework within the Delayed Mirror Descent model.

Findings

Performance degradation is bounded by ( ilde{ ext{O}}(rac{ ext{d}^3}{T}))

INS can maintain Wardrop equilibrium despite bounded delay attacks

Insights for designing resilient transportation systems against jamming attacks

Abstract

\textit{Intelligent Navigation Systems} (INS) are exposed to an increasing number of informational attack vectors, which often intercept through the communication channels between the INS and the transportation network during the data collecting process. To measure the resilience of INS, we use the concept of a Wardrop Non-Equilibrium Solution (WANES), which is characterized by the probabilistic outcome of learning within a bounded number of interactions. By using concentration arguments, we have discovered that any bounded feedback delaying attack only degrades the systematic performance up to order $\tilde{\mathcal{O}}(\sqrt{{d^3}{T^{-1}}})$ along the traffic flow trajectory within the Delayed Mirror Descent (DMD) online-learning framework. This degradation in performance can occur with only mild assumptions imposed. Our result implies that learning-based INS infrastructures can achieve Wardrop Non-equilibrium even when experiencing a certain period of disruption in the information structure. These findings provide valuable insights for designing defense mechanisms against possible jamming attacks across different layers of the transportation ecosystem.