# Finite-time Guarantees for Byzantine-Resilient Distributed State Estimation with Noisy Measurements

arXiv: https://arxiv.org/abs/1810.10086 · HTML: https://mlsanity.com/paper/1810.10086/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 16 Oct 2018.

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

- [Byzantine Machine Learning Made Easy by Resilient Averaging of Momentums](https://mlsanity.com/paper/2205.12173/) (2022)
- [Byzantine Fault-Tolerance in Federated Local SGD under 2f-Redundancy](https://mlsanity.com/paper/2108.11769/) (2021)
- [Finite Sample Guarantees for Distributed Online Parameter Estimation with Communication Costs](https://mlsanity.com/paper/2209.06678/) (2022)
- [Fast and Robust State Estimation and Tracking via Hierarchical Learning](https://mlsanity.com/paper/2306.17267/) (2023)

## Abstract (arXiv)

This work considers resilient, cooperative state estimation in unreliable multi-agent networks. A network of agents aims to collaboratively estimate the value of an unknown vector parameter, while an em unknown subset of agents suffer Byzantine faults. Faulty agents malfunction arbitrarily and may send out em highly unstructured messages to other agents in the network. As opposed to fault-free networks, reaching agreement in the presence of Byzantine faults is far from trivial. In this paper, we propose a computationally-efficient algorithm that is provably robust to Byzantine faults. At each iteration of the algorithm, a good agent (1) performs a gradient descent update based on noisy local measurements, (2) exchanges its update with other agents in its neighborhood, and (3) robustly aggregates the received messages using coordinate-wise trimmed means. Under mild technical assumptions, we establish that good agents learn the true parameter asymptotically in almost sure sense. We further complement our analysis by proving (high probability) em finite-time convergence rate, encapsulating network characteristics.