ZO-COSMO: Index-Free One-Hop Mixing for Decentralized Zeroth-Order Optimization

Abstract:Sparse communication in decentralized zeroth-order learning requires compatible peer-state coordinates. We characterize this one-hop condition and develop \textsf{ZO-COSMO}, coupling two-query estimation with average-preserving masked consensus using $q$ values per active link. Global supports serve all-neighbor mixing; matching updates require agreement only within each pair. We derive a sharp contraction-per-scalar bound within the matching class and convergence guarantees for the core and sparse-momentum updates. At fixed matching, exact moment identities characterize how shared directions preserve gradient-heterogeneity cancellation and redistribute estimation error and disagreement. Mechanism experiments cover unequal curvatures, noise, and sparse momentum. Further tests span $64$ synthetic agents and eight logical Qwen LoRA workers. At matched payload budgets, Qwen2-7B QNLI gains $3.65$ accuracy points over explicit-index Rand-$k$; edge-local updates gain $3.42$ and $2.53$ points over all-neighbor mixing on eight-worker complete and ring graphs. A matched-first-step ablation gives a $3.92$-point momentum benefit. Seed-aware and same-matching controls distinguish encoding, scheduling, and query correlation.

Machine Learning (cs.LG); Systems and Control (eess.SY); Optimization and Control (math.OC)

arXiv:2609.27199 [cs.LG]

(or arXiv:2609.27199v1 [cs.LG] for this version)

https://doi.org/10.48550/arXiv.2609.27199 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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