Core-Halo Decomposition: Decentralizing Large-Scale Fixed-Point Problems
We study solving large-scale fixed-point equation \(x^\star=\bar F(x^\star)\) with decomposition. Standard strict decomposition assigns each agent a disjoint block and evaluates updates using only owned coordinates. For most operators, however, a block update may depend on variables outside the block. Truncating these dependencies by strict decomposition changes the mean operator and creates structural bias that cannot be removed by more samples, smaller stepsizes, or additional consensus. We therefore propose Core-Halo decomposition, which separates write ownership from read-only evaluation context: each agent updates its own core and reads from an overlapping halo. By aligning the Core-...
| Authors | Haixiang, Yang Xu, Jiefu Zhang et al. |
|---|---|
| Primary category | stat.ML |
| Published | 9 May 2026 |
| Last updated at source | 9 May 2026 |
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