# Taming Convergence for Asynchronous Stochastic Gradient Descent with Unbounded Delay in Non-Convex Learning

arXiv: https://arxiv.org/abs/1805.09470 · HTML: https://mlsanity.com/paper/1805.09470/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 24 May 2018.

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

- [Fast Federated Learning in the Presence of Arbitrary Device Unavailability](https://mlsanity.com/paper/2106.04159/) (2021)
- [Anarchic Federated Learning](https://mlsanity.com/paper/2108.09875/) (2021)
- [Delay-adaptive step-sizes for asynchronous learning](https://mlsanity.com/paper/2202.08550/) (2022)
- [Asynchronous Gradient Play in Zero-Sum Multi-agent Games](https://mlsanity.com/paper/2211.08980/) (2022)
- [How Does Data Freshness Affect Real-time Supervised Learning?](https://mlsanity.com/paper/2208.06948/) (2022)
- [Empowering Federated Learning with Implicit Gossiping: Mitigating Connection Unreliability Amidst Unknown and Arbitrary Dynamics](https://mlsanity.com/paper/2404.10091/) (2024)
- [TensAIR: Real-Time Training of Neural Networks from Data-streams](https://mlsanity.com/paper/2211.10280/) (2022)
- [Asynchronous Sharpness-Aware Minimization For Fast and Accurate Deep Learning](https://mlsanity.com/paper/2503.11147/) (2025)
- [SYNTHESIS: A Semi-Asynchronous Path-Integrated Stochastic Gradient Method for Distributed Learning in Computing Clusters](https://mlsanity.com/paper/2208.08425/) (2022)

## Abstract (arXiv)

Understanding the convergence performance of asynchronous stochastic gradient descent method (Async-SGD) has received increasing attention in recent years due to their foundational role in machine learning. To date, however, most of the existing works are restricted to either bounded gradient delays or convex settings. In this paper, we focus on Async-SGD and its variant Async-SGDI (which uses increasing batch size) for non-convex optimization problems with unbounded gradient delays. We prove o(1/√k) convergence rate for Async-SGD and o(1/k) for Async-SGDI. Also, a unifying sufficient condition for Async-SGD's convergence is established, which includes two major gradient delay models in the literature as special cases and yields a new delay model not considered thus far.