Secure Distributed Optimization Under Gradient Attacks

TL;DR

This paper introduces a robust distributed optimization method, CLIP-VRG, that effectively mitigates arbitrary gradient attacks in multi-agent networks, ensuring convergence to the optimal solution despite adversarial interference.

Contribution

The paper proposes CLIP-VRG, a novel distributed stochastic gradient algorithm combining variance reduction and clipping, with theoretical guarantees against gradient attacks in multi-agent networks.

Findings

CLIP-VRG guarantees convergence under certain attack fractions.

The method is effective on synthetic and real datasets.

A tight bound on the attack fraction for guaranteed convergence.

Abstract

In this paper, we study secure distributed optimization against arbitrary gradient attack in multi-agent networks. In distributed optimization, there is no central server to coordinate local updates, and each agent can only communicate with its neighbors on a predefined network. We consider the scenario where out of $n$ networked agents, a fixed but unknown fraction $\rho$ of the agents are under arbitrary gradient attack in that their stochastic gradient oracles return arbitrary information to derail the optimization process, and the goal is to minimize the sum of local objective functions on unattacked agents. We propose a distributed stochastic gradient method that combines local variance reduction and clipping (CLIP-VRG). We show that, in a connected network, when unattacked local objective functions are convex and smooth, share a common minimizer, and their sum is strongly convex, CLIP-VRG leads to almost sure convergence of the iterates to the exact sum cost minimizer at all agents. We quantify a tight upper bound of the fraction $\rho$ of attacked agents in terms of problem parameters such as the condition number of the associated sum cost that guarantee exact convergence of CLIP-VRG, and characterize its asymptotic convergence rate. Finally, we empirically demonstrate the effectiveness of the proposed method under gradient attacks in both synthetic dataset and image classification datasets.