# Byzantine-Resilient Distributed Optimization of Multi-Dimensional Functions

arXiv: https://arxiv.org/abs/2003.09038 · HTML: https://mlsanity.com/paper/2003.09038/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 19 Mar 2020.

## Built on by (most cited first, 8 of 8)

- [Backdoor Attacks in Peer-to-Peer Federated Learning](https://mlsanity.com/paper/2301.09732/) (2023)
- [On the Tradeoff between Privacy Preservation and Byzantine-Robustness in Decentralized Learning](https://mlsanity.com/paper/2308.14606/) (2023)
- [Byzantine Fault-Tolerance in Federated Local SGD under 2f-Redundancy](https://mlsanity.com/paper/2108.11769/) (2021)
- [Collaborative Linear Bandits with Adversarial Agents: Near-Optimal Regret Bounds](https://mlsanity.com/paper/2206.02834/) (2022)
- [A survey on secure decentralized optimization and learning](https://mlsanity.com/paper/2408.08628/) (2024)
- [Byzantine-Resilient Decentralized Multi-Armed Bandits](https://mlsanity.com/paper/2310.07320/) (2023)
- [Distributed Online Optimization with Byzantine Adversarial Agents](https://mlsanity.com/paper/2109.12340/) (2021)
- [VALID: a Validated Algorithm for Learning in Decentralized Networks with Possible Adversarial Presence](https://mlsanity.com/paper/2405.07316/) (2024)

## Abstract (arXiv)

The problem of distributed optimization requires a group of agents to reach agreement on a parameter that minimizes the average of their local cost functions using information received from their neighbors. While there are a variety of distributed optimization algorithms that can solve this problem, they are typically vulnerable to malicious (or ``Byzantine'') agents that do not follow the algorithm. Recent attempts to address this issue focus on single dimensional functions, or provide analysis under certain assumptions on the statistical properties of the functions at the agents. In this paper, we propose a resilient distributed optimization algorithm for multi-dimensional convex functions. Our scheme involves two filtering steps at each iteration of the algorithm: (1) distance-based and (2) component-wise removal of extreme states. We show that this algorithm can mitigate the impact of up to F Byzantine agents in the neighborhood of each regular node, without knowing the identities of the Byzantine agents in advance. In particular, we show that if the network topology satisfies certain conditions, all of the regular states are guaranteed to asymptotically converge to a bounded region that contains the global minimizer.