Distributed Asynchronous Optimization with Unbounded Delays: How Slow Can You Go?

One of the most widely used training methods for large-scale machine learning problems is distributed asynchronous stochastic gradient descent (DASGD). However, a key issue in its implementation is that of delays: when a worker node asynchronously contributes a gradient update to the master, the global model parameter may have changed, rendering this information stale. In massively parallel computing grids, these delays can quickly add up if a node is saturated, so the convergence of DASGD is uncertain under these conditions. Nevertheless, by using a judiciously chosen quasilinear step-size sequence, we show that it is possible to amortize these delays and achieve global convergence with probability 1, even under polynomially growing delays, reaffirming in this way the successful application of DASGD to large-scale optimization problems.