In distributed training setups that utilize multiple parameter servers to increase aggregate network bandwidth, a hierarchical synchronization strategy is highly effective. This approach structures the communication process hierarchically, allowing the system to efficiently manage the synchronization workload across the expanded infrastructure without creating new communication bottlenecks.

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To overcome the bandwidth bottleneck of a single central parameter server in multi-machine training, the system can be scaled by distributing the parameter synchronization workload across multiple servers. By increasing the number of parameter servers to $$n$$, each server is responsible for storing and updating only a fraction of the parameters, specifically $$\mathcal{O}(1/n)$$. Consequently, the total time required for parameter updates and optimization across $$m$$ workers is reduced to $$\mathcal{O}(m/n)$$. In practice, to achieve constant scaling time regardless of the total number of workers, systems often use the exact same machines simultaneously as both workers and servers.

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