The choice of the tuning parameter in the Lasso is central to its statistical performance in high-dimensional linear regression. Classical consistency theory characterizes the rate of the Lasso tuning parameter, and numerous works provide non-asymptotic guarantees. However, the optimal choice of tuning within a fully non-asymptotic framework remains incompletely understood. In this work, we study tuning regimes under which the Lasso exhibits suboptimal prediction performance, in the sense that it is dominated in mean squared prediction error by a simple refinement. We further examine how structural factors in the design matrix influence the suboptimality phenomenon, and discuss extensions to other estimators and more general noise structures.

翻译：Lasso中调优参数的选择对其在高维线性回归中的统计性能至关重要。经典一致性理论刻画了Lasso调优参数的速率，众多研究提供了非渐近保证。然而，在完全非渐近框架下调优参数的最优选择仍未得到充分理解。本文研究了Lasso在特定调优机制下表现出预测性能次优性的情形——即其均方预测误差被简单改进方法所超越。我们进一步探讨了设计矩阵的结构性因素如何影响该次优现象，并讨论了向其他估计量及更一般噪声结构的扩展。