Big-data applications often involve a vast number of observations and
features, creating new challenges for variable selection and parameter
estimation. This paper presents a novel technique called ``slow kill,'' which
utilizes nonconvex constrained optimization, adaptive $\ell_2$-shrinkage, and
increasing learning rates. The fact that the problem size can decrease during
the slow kill iterations makes it particularly effective for large-scale
variable screening. The interaction between statistics and optimization
provides valuable insights into controlling quantiles, stepsize, and shrinkage
parameters in order to relax the regularity conditions required to achieve the
desired level of statistical accuracy. Experimental results on real and
synthetic data show that slow kill outperforms state-of-the-art algorithms in
various situations while being computationally efficient for large-scale data.

本文介绍了一种称为 “slow kill” 的新技术，它利用了非凸约束优化、自适应规则化和动态学习率的方法来解决大规模变量筛选的问题，并且实验证明了其优越性。

大数据学习的缓慢杀死

Slow Kill for Big Data Learning

We consider nonconvex constrained optimization problems and propose a new
approach to the convergence analysis based on penalty functions. We make use of
classical penalty functions in an unconventional way, in that penalty functions
only enter in the theoretical analysis of convergence while the algorithm
itself is penalty-free. Based on this idea, we are able to establish several
new results, including the first general analysis for diminishing stepsize
methods in nonconvex, constrained optimization, showing convergence to
generalized stationary points, and a complexity study for SQP-type algorithms.

本文针对非凸约束优化问题，提出一种基于罚函数的新收敛分析方法。我们以传统罚函数的非常规方式进行研究，只将罚函数应用于收敛性理论分析中，而算法本身无需使用罚函数。基于此思想，我们得到了若干新结果，包括第一个针对非凸约束优化的递减步长方法收敛到广义稳定点的一般分析，以及 SQP 类型算法的复杂性研究。