Bridging the Gap Between Homogeneous and Heterogeneous Asynchronous Optimization Is Surprisingly Difficult

2026-09-15

AI Summary

本文探讨了异构异步优化中的时间复杂度问题，通过引入强插值和局部Polyak-Lojasiewicz条件，提出了新的时间复杂度界限，缩小了与同构设置的差距。

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.

Problem

• asynchronous optimization
• heterogeneous setting
• homogeneous setting
• time complexity

Innovation

• strong interpolation
• local Polyak-Lojasiewicz condition
• heterogeneous setting