# A Resilient Convex Combination for consensus-based distributed algorithms

arXiv: https://arxiv.org/abs/1806.10271 · HTML: https://mlsanity.com/paper/1806.10271/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 27 Jun 2018.

## Built on by (most cited first, 3 of 3)

- [A survey on secure decentralized optimization and learning](https://mlsanity.com/paper/2408.08628/) (2024)
- [ImprovDML: Improved Trade-off in Private Byzantine-Resilient Distributed Machine Learning](https://mlsanity.com/paper/2506.15181/) (2025)
- [Centroid Approximation for Byzantine-Tolerant Federated Learning](https://mlsanity.com/paper/2506.15264/) (2025)

## Abstract (arXiv)

Consider a set of vectors in ℝn, partitioned into two classes: normal vectors and malicious vectors. The number of malicious vectors is bounded but their identities are unknown. The paper provides a way for achieving a resilient convex combination, which is a convex combination of only normal vectors. Compared with existing approaches based on Tverberg points, the proposed method based on the intersection of convex hulls has lower computational complexity. Simulations suggest that the proposed method can be applied to resilience for consensus-based distributed algorithms against Byzantine attacks.