## Asynchronous Stochastic Optimization Robust to Arbitrary Delays

May 21, 2021 (edited Jan 23, 2022)NeurIPS 2021 PosterReaders: Everyone
• Keywords: Stochastic Optimization, Asynchronous Optimization, Delayed Gradients
• TL;DR: In stochastic optimization with delayed gradients, we provide a new algorithm with convergence rate that depends on the average delay rather than on the (current state-of-the-art) maximal delay.
• Abstract: We consider the problem of stochastic optimization with delayed gradients in which, at each time step $t$, the algorithm makes an update using a stale stochastic gradient from step $t - d_t$ for some arbitrary delay $d_t$. This setting abstracts asynchronous distributed optimization where a central server receives gradient updates computed by worker machines. These machines can experience computation and communication loads that might vary significantly over time. In the general non-convex smooth optimization setting, we give a simple and efficient algorithm that requires $O( \sigma^2/\epsilon^4 + \tau/\epsilon^2 )$ steps for finding an $\epsilon$-stationary point $x$. Here, $\tau$ is the \emph{average} delay $\frac{1}{T}\sum_{t=1}^T d_t$ and $\sigma^2$ is the variance of the stochastic gradients. This improves over previous work, which showed that stochastic gradient decent achieves the same rate but with respect to the \emph{maximal} delay $\max_{t} d_t$, that can be significantly larger than the average delay especially in heterogeneous distributed systems. Our experiments demonstrate the efficacy and robustness of our algorithm in cases where the delay distribution is skewed or heavy-tailed.
• Code Of Conduct: I certify that all co-authors of this work have read and commit to adhering to the NeurIPS Statement on Ethics, Fairness, Inclusivity, and Code of Conduct.
15 Replies