  Distributed optimization is vital in solving large-scale machine learning
problems. A widely-shared feature of distributed optimization techniques is the
requirement that all nodes complete their assigned tasks in each computational
epoch before the system can proceed to the next epoch. In such settings, slow
nodes, called stragglers, can greatly slow progress. To mitigate the impact of
stragglers, we propose an online distributed optimization method called Anytime
Minibatch. In this approach, all nodes are given a fixed time to compute the
gradients of as many data samples as possible. The result is a variable
per-node minibatch size. Workers then get a fixed communication time to average
their minibatch gradients via several rounds of consensus, which are then used
to update primal variables via dual averaging. Anytime Minibatch prevents
stragglers from holding up the system without wasting the work that stragglers
can complete. We present a convergence analysis and analyze the wall time
performance. Our numerical results show that our approach is up to 1.5 times
faster in Amazon EC2 and it is up to five times faster when there is greater
variability in compute node performance.
