Bridging the Gap Between Homogeneous and Heterogeneous Asynchronous Optimization Is Surprisingly Difficult
Abstract
Modern large-scale machine learning tasks often require multiple workers, devices, CPUs, or GPUs to compute stochastic gradients in parallel and asynchronously to train model weights. Theoretical results typically distinguish between two settings: (i) the homogeneous setting, where all workers have access to the same data distribution, and (ii) the heterogeneous setting, where each worker operates on different data distributions. Known optimal time complexities in these settings reveal a significant gap, with far more pessimistic guarantees in the heterogeneous case. In this work, we investigate whether these pessimistic optimal time complexities can be overcome under different assumptions. Surprisingly, we show that improvement is provably impossible under widely used first- and second-order similarity assumptions for any randomized algorithm. We then turn to the interpolation regime and demonstrate that the weak interpolation assumption alone is also insufficient. Finally, we introduce a minimal combination of irreducible assumptions, strong interpolation and the local Polyak-Lojasiewicz condition, to derive a new time complexity bound that matches the dependence on worker computation times in the best-known result in the homogeneous setting, without requiring identical data distributions.
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BibTeX
@misc{tyurin2026bridging,
title = {{Bridging the Gap Between Homogeneous and Heterogeneous Asynchronous Optimization Is Surprisingly Difficult}},
author = {Alexander Tyurin},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.17483},
eprint = {2609.17483},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.17483},
}
RIS
TY - UNPB
TI - Bridging the Gap Between Homogeneous and Heterogeneous Asynchronous Optimization Is Surprisingly Difficult
AU - Alexander Tyurin
PY - 2026
DA - 2026/09/15
PB - arXiv
DO - 10.48550/arxiv.2609.17483
UR - https://arxiv.org/abs/2609.17483
AB - Modern large-scale machine learning tasks often require multiple workers, devices, CPUs, or GPUs to compute stochastic gradients in parallel and asynchronously to train model weights. Theoretical results typically distinguish between two settings: (i) the homogeneous setting, where all workers have access to the same data distribution, and (ii) the heterogeneous setting, where each worker operates on different data distributions. Known optimal time complexities in these settings reveal a significant gap, with far more pessimistic guarantees in the heterogeneous case. In this work, we investigate whether these pessimistic optimal time complexities can be overcome under different assumptions. Surprisingly, we show that improvement is provably impossible under widely used first- and second-order similarity assumptions for any randomized algorithm. We then turn to the interpolation regime and demonstrate that the weak interpolation assumption alone is also insufficient. Finally, we introduce a minimal combination of irreducible assumptions, strong interpolation and the local Polyak-Lojasiewicz condition, to derive a new time complexity bound that matches the dependence on worker computation times in the best-known result in the homogeneous setting, without requiring identical data distributions.
ER -