Interpretation of infinite-sum matrix-norm quantities in stochastic Push–Pull analysis

Clarify the meaning and theoretical role of the infinite sums of matrix-norm terms used in stochastic Push–Pull convergence analyses.

Background

The paper surveys network descriptors used in directed decentralized optimization. It notes that a stochastic Push–Pull analysis uses infinite sums of matrix-norm terms to encompass several existing algorithms, but does not provide a clear interpretation of what these quantities represent or how they should be understood as network-complexity measures. Establishing their meaning could improve the conceptual and comparative understanding of convergence guarantees for stochastic Push–Pull methods.

References

A recent stochastic Push--Pull analysis uses infinite sums of matrix-norm terms to encompass several existing algorithms, although the meaning of these quantities remains unclear.

— Optimal Network Dependence in Distributed Stochastic Optimization via Tree Routing  (2609.18101 - You et al., 16 Sep 2026) in Section 1, subsection “Related Work”