发表机构
Nanjing University of Aeronautics and Astronautics（南京航空航天大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出细粒度随机批量采样坐标下降框架，推导列缩放不变的收敛界，并设计学习式采样策略，在CT重建中显著加速收敛并优于现有方法。
AI 中文摘要
本文通过引入坐标级批量采样分布特征，改进了随机块坐标下降方法，提出了一种细粒度的随机批量采样坐标下降框架，该框架适用于在任意静态随机采样规则下求解大规模线性最小二乘问题的任何块坐标下降方法。基于此框架，我们推导出新的线性收敛速率界，这些界对数据矩阵的列缩放具有不变性。理论分析和数值实验验证了新界显著优于现有结果，并且与实际收敛速率更加吻合。此外，我们提出了一种基于学习的采样策略，通过参数化批量采样分布并利用基于梯度的训练优化其参数。在计算机断层扫描（CT）重建问题上的初步数值结果表明，所提方法的收敛速度显著快于使用其他固定采样规则的变体，并且在计算效率上优于测试的自适应坐标下降方法和全梯度下降方法，证实了学习到的采样分布能够有效捕获问题特定结构，从而在框架内加速收敛。
英文摘要
This paper refines randomized block coordinate descent by introducing a coordinate-level batch-sampling distribution characterization, yielding a fine-grained randomized batch-sampling coordinate descent framework, which applies to any block coordinate descent method under an arbitrary static stochastic sampling rule for solving large-scale linear least-squares problems. Based on this framework, we derive new linear convergence rate bounds that are invariant to the column scaling of data matrices. Theoretical analysis and numerical experiments validate that the new bounds are significantly sharper than existing results and better aligned with the practical convergence rate. Furthermore, we proposed a learning-based sampling strategy by parameterizing the batch-sampling distribution and optimizing its parameters through gradient-based training. Preliminary numerical results on computed tomography (CT) reconstruction problems demonstrate that the resulting method converges significantly faster than variants using other fixed sampling rules, and outperforms tested adaptive coordinate descent methods and full gradient descent in computational efficiency, confirming that learned sampling distributions can effectively capture problem-specific structure to accelerate convergence within the framework.
