Convergence of Byzantine-Resilient Gradient Tracking via Probabilistic Edge Dropout

• URL: http://arxiv.org/abs/2604.00449v2
• Date: Sat, 04 Apr 2026 05:44:27 GMT
• Title: Convergence of Byzantine-Resilient Gradient Tracking via Probabilistic Edge Dropout
• Abstract summary: We study distributed optimization over networks with Byzantine agents that may send arbitrary adversarial messages.<n>We propose emphGradient Tracking with Probabilistic Edge Dropout and Leaky Integration (GT-PD-L)<n>GT-PD-L outperforms coordinate-wise mean by up to 4.3 percentage points under stealth attacks.
• Score: 1.3902537392439644
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We study distributed optimization over networks with Byzantine agents that may send arbitrary adversarial messages. We propose \emph{Gradient Tracking with Probabilistic Edge Dropout} (GT-PD), a stochastic gradient tracking method that preserves the convergence properties of gradient tracking under adversarial communication. GT-PD combines two complementary defense layers: a universal self-centered projection that clips each incoming message to a ball of radius $τ$ around the receiving agent, and a fully decentralized probabilistic dropout rule driven by a dual-metric trust score in the decision and tracking channels. This design bounds adversarial perturbations while preserving the doubly stochastic mixing structure, a property often lost under robust aggregation in decentralized settings. Under complete Byzantine isolation ($p_b=0$), GT-PD converges linearly to a neighborhood determined solely by stochastic gradient variance. For partial isolation ($p_b>0$), we introduce \emph{Gradient Tracking with Probabilistic Edge Dropout and Leaky Integration} (GT-PD-L), which uses a leaky integrator to control the accumulation of tracking errors caused by persistent perturbations and achieves linear convergence to a bounded neighborhood determined by the stochastic variance and the clipping-to-leak ratio. We further show that under two-tier dropout with $p_h=1$, isolating Byzantine agents introduces no additional variance into the honest consensus dynamics. Experiments on MNIST under Sign Flip, ALIE, and Inner Product Manipulation attacks show that GT-PD-L outperforms coordinate-wise trimmed mean by up to 4.3 percentage points under stealth attacks.

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