Bottleneck Communication Delay Minimization for Communication-Efficient Decentralized Learning

For communication-efficient decentralized learning, advanced network (NW) topologies, such as exponential and 1-peer exponential graphs, have been studied under homogeneous communication delays. However, real-world NWs exhibit heterogeneous communication delays, making node assignment optimization crucial for minimizing the Bottleneck Communication Delay (BCD). We propose BTSP-MSR, an approximate method for minimizing BCD on circulant digraphs, including exponential and 1-peer exponential graphs. Leveraging the fact that circulant digraphs can be viewed as a union of (directed) ring graphs, we derive an upper bound on the BCD by combining the ring-graph BCD (BTSP) with a deviation term (MSR). We then construct a solver that sequentially minimizes these two terms. Numerical experiments show that BTSP-MSR consistently reduces BCD across several circulant digraphs with large numbers of nodes. Notably, incorporating the exponential or 1-peer exponential graph enables communication-efficient decentralized learning under heterogeneous delay settings.