
Since hierarchical SGD is less well-studied than local SGD, there is no guarantee that hierarchical SGD with a finer-grained synchronization granularity can converge faster than certain advanced forms of local SGD, such as SlowMo, which can improve convergence efficiency with slow momentum. However, to the best of our knowledge, these advanced algorithms cannot be natively supported as a PyTorch DDP plugin like hierarchical SGD yet.

Acknowledgements
We would like to thank Cruise teammates Bo Tian, Sergei Vorobev, Eugene Selivonchyk, Tsugn-Hsien Lee, Dan Ring, Ian Ackerman, Lei Chen, Maegan Chew, Viet Anh To, Xiaohui Long, Zeyu Chen, Alexander Sidorov, Igor Tsvetkov, Xin Hu, Manav Kataria, Marina Rubtsova, and Mohamed Fawzy, as well as Meta teammates Shen Li, Yanli Zhao, Suraj Subramanian, Hamid Shojanzeri, Anjali Sridhar and Bernard Nguyen for the support.