Converting ADMM to a Proximal Gradient for Convex Optimization Problems
Converting ADMM to a Proximal Gradient for Convex Optimization Problems
复制标题
将 ADMM 转换为凸优化问题的近似梯度
DOI：
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发表时间：
2021
期刊：
影响因子：
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通讯作者：
J. Suzuki
中科院分区：
文献类型：
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作者：
Ryosuke Shimmura;J. Suzuki
在机器学习和数据科学中，我们经常认为ffi是解决问题的效率。在稀疏估计中，如融合套索和凸聚类，我们使用近似梯度法或乘子交替方向法(ADMM)来解决这个问题。在前一种情况下，将矩阵除法包括在内需要时间，而在后一种情况下，已经发展了一种有效的方法，如FISTA(快速迭代收缩阈值算法)。在假设约束和目标是强凸的情况下，提出了一种将ADMM解转化为近似梯度法的一般方法。然后，我们将其应用于稀疏估计问题，如稀疏凸聚类和趋势fi估计问题，并通过数值实验表明，我们可以在效率方面获得显著的fiCan改善。
: In machine learning and data science, we often consider efficiency for solving problems. In sparse estimation, such as fused lasso and convex clustering, we apply either the proximal gradient method or the alternating direction method of multipliers (ADMM) to solve the problem. It takes time to include matrix division in the former case, while an efficient method such as FISTA (fast iterative shrinkage-thresholding algorithm) has been developed in the latter case. This paper proposes a general method for converting the ADMM solution to the proximal gradient method, assuming that the constraints and objectives are strongly convex. Then, we apply it to sparse estimation problems, such as sparse convex clustering and trend filtering, and we show by numerical experiments that we can obtain a significant improvement in terms of efficiency.