Reconciling Communication Compression and Byzantine-Robustness in Distributed Learning

Distributed learning enables scalable model training over decentralized data, but remains hindered by Byzantine faults and high communication costs. While both challenges have been studied extensively in isolation, their interplay has received limited attention. Prior work has shown that naively combining communication compression with Byzantine-robust aggregation can severely weaken resilience to faulty nodes. The current state-of-the-art, Byz-DASHA-PAGE, leverages a momentum-based variance reduction scheme to counteract the negative effect of compression noise on Byzantine robustness. In this work, we introduce RoSDHB, a new algorithm that integrates classical Polyak momentum with a coordinated compression strategy. Theoretically, RoSDHB matches the convergence guarantee of Byz-DASHA-PAGE under the standard $(G, B)$-gradient dissimilarity model, but relies on milder assumptions. Empirically, RoSDHB demonstrates stronger robustness while achieving substantial communication savings compared to Byz-DASHA-PAGE.