LoRDO: Distributed Low-Rank Optimization with Infrequent Communication

Distributed training of foundation models via textttDDP is limited by interconnect bandwidth. While infrequent communication strategies reduce synchronization frequency, they remain bottlenecked by the memory and communication requirements of optimizer states. Low-rank optimizers can alleviate these constraints; however, in the local-update regime, workers lack access to the full-batch gradients required to compute low-rank projections, which degrades performance. We propose textttLoRDO, a principled framework unifying low-rank optimization with infrequent synchronization. We first demonstrate that, while global projections based on pseudo-gradients are theoretically superior, they permanently restrict the optimization trajectory to a low-rank subspace. To restore subspace exploration, we introduce a full-rank quasi-hyperbolic update. textttLoRDO achieves near-parity with low-rank textttDDP in language modeling and downstream tasks at model scales of 125M--720M, while reducing communication by ≈ 10 ×. Finally, we show that textttLoRDO improves performance even more in very low-memory settings with small rank/batch size.