# Byzantine-Resilient Multi-Agent Distributed Exact Optimization with Less Data

## TL;DR

This paper introduces a Byzantine-resilient distributed optimization algorithm that does not require fully connected communication topology, ensuring convergence under Byzantine attacks with less data exchange.

## Contribution

It proposes a novel distributed comparative gradient elimination algorithm that tolerates Byzantine faults without full connectivity, improving robustness and efficiency.

## Key findings

- All normal agents reach consensus and converge to the optimal solution.
- The algorithm works under less restrictive network connectivity conditions.
- Numerical experiments verify the theoretical convergence and robustness.

## Abstract

This paper studies the distributed multi-agent resilient optimization problem under the f-total Byzantine attacks. Compared with the previous work on Byzantineresilient multi-agent exact optimization problems, we do not require the communication topology to be fully connected. Under the redundancy of cost functions, we propose the distributed comparative gradient elimination resilient optimization algorithm based on the traditional assumptions on strongly convex global costs and Lipschitz continuous gradients. Under this algorithm, we successfully prove that if the number of inneighbors of each normal agent is greater than some constant and the parameter f satisfies certain conditions, all normal agents' local estimations of the global variable will finally reach consensus and converge to the optimized solution. Finally, the numerical experiments successfully verify the correctness of the results.

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Source: https://tomesphere.com/paper/2302.14570