Finite-Time Guarantees for Byzantine-Resilient Distributed State Estimation With Noisy Measurements

Abstract

This work considers resilient, cooperative state estimation in unreliable multi-agent networks. A network of agents aims to collaboratively estimate the value of an unknown vector parameter, while an unknown subset of agents suffer Byzantine faults. Faulty agents malfunction arbitrarily and may send out highly unstructured messages to other agents in the network. As opposed to fault-free networks, reaching agreement in the presence of Byzantine faults is far from trivial. In this paper, we propose a computationally-efficient algorithm that is provably robust to Byzantine faults. At each iteration of the algorithm, a good agent (1) performs a gradient descent update based on noisy local measurements, (2) exchanges its update with other agents in its neighborhood, and (3) robustly aggregates the received messages using coordinate-wise trimmed means. Under mild technical assumptions, we establish that good agents learn the true parameter asymptotically in almost sure sense. We further complement our analysis by proving (high probability) finite-time convergence rate, encapsulating network characteristics.

Adversarial Robustness in Cognitive Radio Networks

“…In [15] as the first single-server byzantine-resilient scheme for secure federated learning based on an integrated stochastic quantisation, some important trade-offs were examined for the network size, privacy protection and user dropouts. In [16], the asymptotically learning issue of the true hypothesis in an almost sure sense was explored. In [17], it was perfectly proven that the probability of sample paths through which the rejection rate of false observations tangentially passes from the mean-rate, would theoretically experience an exponential plummet.…”

“…Therefore, one can assign an unknown random variable 𝜉 𝑏 ∈ [0, 1) coordinated by the Byzantines 15 where we aim at maximising the synchronisability. This maximisation can be fully performed according to non-convex optimisation algorithms such as the Simultaneous Perturbation Stochastic Approximation (SPSA) method 16 where Δ 𝑛 is a random perturbation vector whose elements are Bernoulli disributed 17 , and w.r.t. the term 𝒞 𝑛 as the hyperparameter for the SPSA 18 , and the term 𝑛 is the index of the iteration.…”

On the Computational Complexity of the Secure State-Reconstruction Problem

“…The distributed version of the SSR problem has also attracted a substantial amount of interest given the distributed nature of CPSs. Several authors have studied the problem of estimating a static vector from a set of corrupted measurements, either over a distributed sensor network [21,22], or over a connected-on-average network [23]. A control-theoretic approach to distributed function calculation was developed in [12].…”

Genuinely Distributed Byzantine Machine Learning

“…Byzantine-resilient ML. Over the past three years, a growing body of work, e.g., [5,9,12,16,20,46,48,51], took up the challenge of Byzantine-resilient ML. The Byzantine failure model, as originally introduced in distributed computing [32], encompasses crashes, software bugs, hardware defects, message omissions, corrupted data, and even worse, hacked machines [10,49].…”