Asynchronous Stochastic Optimization Robust to Arbitrary Delays

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(σ²/ϵ⁴ + τ/ϵ²) steps for finding an ϵ-stationary point x, where τ is the average delay_T¹∑^T_t=1 d_t and σ² 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 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.