Tao Li

Yan Chen, Tao Li, Xiaofeng Zong

We study the distributed optimization problem over a graphon with a continuum of nodes, which is regarded as the limit of the distributed networked optimization as the number of nodes goes to infinity. Each node has a private local cost function. The global cost function, which all nodes cooperatively minimize, is the integral of the local cost functions on the node set. We propose stochastic gradient descent and gradient tracking algorithms over the graphon. We establish a general lemma for the upper bound estimation related to a class of time-varying differential inequalities with negative linear terms, based upon which, we prove that for both kinds of algorithms, the second moments of the nodes' states are uniformly bounded. Especially, for the stochastic gradient tracking algorithm, we transform the convergence analysis into the asymptotic property of coupled nonlinear differential inequalities with time-varying coefficients and develop a decoupling method. For both kinds of algorithms, we show that by choosing the time-varying algorithm gains properly, all nodes' states achieve $\mathcal{L}^{\infty}$-consensus for a connected graphon. Furthermore, if the local cost functions are strongly convex, then all nodes' states converge to the minimizer of the global cost function and the auxiliary states in the stochastic gradient tracking algorithm converge to the gradient value of the global cost function at the minimizer uniformly in mean square.

Xingyu Lyu, Ning Wang, Yang Xiao et al.

Federated Learning is a popular paradigm that enables remote clients to jointly train a global model without sharing their raw data. However, FL has been shown to be vulnerable towards model poisoning attacks due to its distributed nature. Particularly, attackers acting as participants can upload arbitrary model updates that effectively compromise the global model of FL. While extensive research has been focusing on fighting against these attacks, we find that most of them assume data at remote clients are under iid while in practice they are inevitably non-iid. Our benchmark evaluations reveal that existing defenses generally fail to live up to their reputation when applied to various non-iid scenarios. In this paper, we propose a novel approach, GeminiGuard, that aims to address such a significant gap. We design GeminiGuard to be lightweight, versatile, and unsupervised so that it aligns well with the practical requirements of deploying such defenses. The key challenge from non-iids is that they make benign model updates look more similar to malicious ones. GeminiGuard is mainly built on two fundamental observations: (1) existing defenses based on either model-weight analysis or latent-space analysis face limitations in covering different MPAs and non-iid scenarios, and (2) model-weight and latent-space analysis are sufficiently different yet potentially complementary methods as MPA defenses. We hence incorporate a novel model-weight analysis component as well as a custom latent-space analysis component in GeminiGuard, aiming to further enhance its defense performance. We conduct extensive experiments to evaluate our defense across various settings, demonstrating its effectiveness in countering multiple types of untargeted and targeted MPAs, including adaptive ones. Our comprehensive evaluations show that GeminiGuard consistently outperforms SOTA defenses under various settings.