Byzantine-Robust Muon: Resilient Momentum Orthogonalization for Distributed Learning

arXiv:2611.13137v1 Announce Type: new Abstract: Optimization methods, including the Muon optimizer based on the Linear Minimization Oracle (LMO) and momentum orthogonalization, have shown strong empirical performance in large-scale and distributed learning, yet their robustness to adversarial behavior and data heterogeneity is not well understood. We study these methods within a unified first-order trust-region framework and analyze Muon-based updates with robust aggregation for Byzantine-robust distributed and federated learning. Our analysis does not rely on the i.i.d. assumption and introduces a non-Euclidean notion of heterogeneity consistent with the trust-region geometry. Under this framework, we establish convergence guarantees for both general non-convex and star-convex objectives.