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

arXiv: https://arxiv.org/abs/2304.01161 · HTML: https://mlsanity.com/paper/2304.01161/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 21 references that are in the map.
- First posted on arXiv 3 Apr 2023.

## Builds on (most cited first, 7 of 7)

- [Online Learning under Delayed Feedback](https://mlsanity.com/paper/1306.0686/) (2013)
- [The Confluence of Networks, Games and Learning](https://mlsanity.com/paper/2105.08158/) (2021)
- [Online Learning with Local Permutations and Delayed Feedback](https://mlsanity.com/paper/1703.04274/) (2017)
- [On the Resilience of Traffic Networks under Non-Equilibrium Learning](https://mlsanity.com/paper/2210.03214/) (2022)
- [Efficient Episodic Learning of Nonstationary and Unknown Zero-Sum Games Using Expert Game Ensembles](https://mlsanity.com/paper/2107.13632/) (2021)
- [On Poisoned Wardrop Equilibrium in Congestion Games](https://mlsanity.com/paper/2209.00094/) (2022)
- [High Probability Convergence for Accelerated Stochastic Mirror Descent](https://mlsanity.com/paper/2210.00679/) (2022)

## Built on by (most cited first, 4 of 4)

- [Symbiotic Game and Foundation Models for Cyber Deception Operations in Strategic Cyber Warfare](https://mlsanity.com/paper/2403.10570/) (2024)
- [Self-Confirming Transformer for Belief-Conditioned Adaptation in Offline Multi-Agent Reinforcement Learning](https://mlsanity.com/paper/2310.04579/) (2023)
- [Reinforcement Learning with Physics-Informed Symbolic Program Priors for Zero-Shot Wireless Indoor Navigation](https://mlsanity.com/paper/2506.22365/) (2025)
- [Distributed Online Convex Optimization with Nonseparable Costs and Constraints](https://mlsanity.com/paper/2602.10452/) (2026)

## Abstract (arXiv)

textitIntelligent 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 tildeO(√d3T-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.