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.

本篇论文提出一种基于分布式环境中的 L1 正则化优化问题的通信高效框架，通过将经典目标在更一般的原始对偶设定中进行观察，我们开发了一类新方法，能够有效地分布式和应用于常见的稀疏性诱导模型。

L1 正则化分布式优化：一种高效的对偶原始框架

L1-Regularized Distributed Optimization: A Communication-Efficient  Primal-Dual Framework

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.

提出了一种称为 CoCoA 的通信高效的框架，该框架采用原始 - 对偶设置进行本地计算，从而显著减少必要的通信，实验结果表明，相比于 SGD 和 SDCA 算法，CoCoA 在平均 25 倍的时间内收敛到相同的.001 精度解决方案质量。