  Communication remains the most significant bottleneck in the performance of
distributed optimization algorithms for large-scale machine learning. In this
paper, we propose a communication-efficient framework, CoCoA, that uses local
computation in a primal-dual setting to dramatically reduce the amount of
necessary communication. We provide a strong convergence rate analysis for this
class of algorithms, as well as experiments on real-world distributed datasets
with implementations in Spark. In our experiments, we find that as compared to
state-of-the-art mini-batch versions of SGD and SDCA algorithms, CoCoA
converges to the same .001-accurate solution quality on average 25x as quickly.
