Asynchronous Stochastic Optimization Robust to Arbitrary Delays
This addresses optimization in heterogeneous distributed systems where delays vary, offering more efficient convergence for machine learning practitioners dealing with asynchronous updates.
The paper tackles stochastic optimization with arbitrary delayed gradients, common in asynchronous distributed settings, by proposing an algorithm that achieves an $O(σ^2/ε^4 + τ/ε^2)$ rate for finding an $ε$-stationary point, where $τ$ is the average delay, improving over prior work that depended on the maximal delay.
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 non-convex smooth optimization setting, we give a simple and efficient algorithm that requires $O( σ^2/ε^4 + τ/ε^2 )$ steps for finding an $ε$-stationary point $x$, where $τ$ is the \emph{average} delay $\smash{\frac{1}{T}\sum_{t=1}^T d_t}$ and $σ^2$ 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.