  Despite the importance of sparsity in many large-scale applications, there
are few methods for distributed optimization of sparsity-inducing objectives.
In this paper, we present a communication-efficient framework for
L1-regularized optimization in the distributed environment. By viewing
classical objectives in a more general primal-dual setting, we develop a new
class of methods that can be efficiently distributed and applied to common
sparsity-inducing models, such as Lasso, sparse logistic regression, and
elastic net-regularized problems. We provide theoretical convergence guarantees
for our framework, and demonstrate its efficiency and flexibility with a
thorough experimental comparison on Amazon EC2. Our proposed framework yields
speedups of up to 50x as compared to current state-of-the-art methods for
distributed L1-regularized optimization.
