# Tight Time Complexities in Parallel Stochastic Optimization with Arbitrary Computation Dynamics

arXiv: https://arxiv.org/abs/2408.04929 · HTML: https://mlsanity.com/paper/2408.04929/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 9 Aug 2024.

## Built on by (most cited first, 9 of 9)

- [Ringmaster ASGD: The First Asynchronous SGD with Optimal Time Complexity](https://mlsanity.com/paper/2501.16168/) (2025)
- [Ringleader ASGD: The First Asynchronous SGD with Optimal Time Complexity under Data Heterogeneity](https://mlsanity.com/paper/2509.22860/) (2025)
- [Optimal Asynchronous Stochastic Nonconvex Optimization under Heavy-Tailed Noise](https://mlsanity.com/paper/2601.19379/) (2026)
- [Rescaled Asynchronous SGD: Optimal Distributed Optimization under Data and System Heterogeneity](https://mlsanity.com/paper/2605.13434/) (2026)
- [Ringmaster LMO: Asynchronous Linear Minimization Oracle Momentum Method](https://mlsanity.com/paper/2605.18174/) (2026)
- [Faster Stochastic Optimization with Arbitrary Delays via Asynchronous Mini-Batching](https://mlsanity.com/paper/2408.07503/) (2024)
- [Do We Need Asynchronous SGD? On the Near-Optimality of Synchronous Methods](https://mlsanity.com/paper/2602.03802/) (2026)
- [Rennala MVR: Improved Time Complexity for Parallel Stochastic Optimization via Momentum-Based Variance Reduction](https://mlsanity.com/paper/2605.08871/) (2026)
- [Beyond Aggregate Drift: Optimal Client-Specific Windows in Federated Learning](https://mlsanity.com/paper/2610.15543/) (2026)

## Abstract (arXiv)

In distributed stochastic optimization, where parallel and asynchronous methods are employed, we establish optimal time complexities under virtually any computation behavior of workers/devices/CPUs/GPUs, capturing potential disconnections due to hardware and network delays, time-varying computation powers, and any possible fluctuations and trends of computation speeds. These real-world scenarios are formalized by our new universal computation model. Leveraging this model and new proof techniques, we discover tight lower bounds that apply to virtually all synchronous and asynchronous methods, including Minibatch SGD, Asynchronous SGD (Recht et al., 2011), and Picky SGD (Cohen et al., 2021). We show that these lower bounds, up to constant factors, are matched by the optimal Rennala SGD and Malenia SGD methods (Tyurin & Richt'arik, 2023).