Core-Halo Decomposition: Decentralizing Large-Scale Fixed-Point Problems

Researchers have introduced Core-Halo decomposition, a novel method for solving large-scale fixed-point equations in decentralized multi-agent systems. Traditional strict decomposition assigns disjoint blocks to agents, often truncating dependencies and creating structural bias that cannot be corrected by standard optimization techniques. The proposed Core-Halo approach separates write ownership from read-only evaluation contexts, allowing agents to update their core variables while reading from an overlapping halo. This alignment with the block-dependence structure ensures faithful implementation of the original fixed-point problem. The study characterizes the limitations of strict decomposition through a Bellman closure condition and establishes a blockwise bias lower bound. Extensive experiments demonstrate that Core-Halo decomposition achieves performance near that of centralized systems while retaining the parallelism benefits of decentralization. This advancement addresses fundamental obstructions in distributed computing and machine learning, offering a robust solution for complex operator evaluations without sacrificing computational efficiency or accuracy.