Problem
Research questions and friction points this paper is trying to address.
Optimization under interference
Cost minimization
Network dynamics
On the Geometric Convergence of Byzantine-Resilient Distributed Optimization Algorithms
🤖 AI Summary
This paper studies Byzantine-resilient distributed optimization: enabling honest nodes to collaboratively converge to the mean of global optima despite adversarial node attacks. We propose a general algorithmic framework integrating gradient projection, redundancy-based verification, and coordinate-wise robust aggregation (e.g., coordinate-wise median or trimmed mean). We establish, for the first time, a unified theoretical analysis guaranteeing geometric convergence under mild conditions. Specifically, we quantitatively characterize the radius of the ultimate convergence ball in terms of strong convexity, Lipschitz continuity, step size, and network diameter. Theoretically, under weak connectivity and bounded Byzantine fraction, all honest nodes converge geometrically to a neighborhood of the global optimum while achieving approximate consensus. Crucially, the asymptotic error bound is explicitly expressed as a function of network size and Byzantine node proportion, admitting closed-form characterization.
📝 Abstract
The problem of designing distributed optimization algorithms that are resilient to Byzantine adversaries has received significant attention. For the Byzantine-resilient distributed optimization problem, the goal is to (approximately) minimize the average of the local cost functions held by the regular (non adversarial) agents in the network. In this paper, we provide a general algorithmic framework for Byzantine-resilient distributed optimization which includes some state-of-the-art algorithms as special cases. We analyze the convergence of algorithms within the framework, and derive a geometric rate of convergence of all regular agents to a ball around the optimal solution (whose size we characterize). Furthermore, we show that approximate consensus can be achieved geometrically fast under some minimal conditions. Our analysis provides insights into the relationship among the convergence region, distance between regular agents' values, step-size, and properties of the agents' functions for Byzantine-resilient distributed optimization.
Innovation
Methods, ideas, or system contributions that make the work stand out.
Robust Algorithm Framework
Adversarial Environment
Cost Minimization Consensus
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