Asynchronous Stochastic Optimization Robust to Arbitrary Delays
Abstract
We consider stochastic optimization with delayed gradients where, 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 nonconvex 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 $x$, where $\tau$ is the \emph{average} delay $\smash{\frac{1}{T}\sum_{t=1}^T d_t}$ 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 heavytailed.
 Publication:

arXiv eprints
 Pub Date:
 June 2021
 arXiv:
 arXiv:2106.11879
 Bibcode:
 2021arXiv210611879C
 Keywords:

 Mathematics  Optimization and Control;
 Computer Science  Machine Learning