论文标题
坐标下降的模型识别和局部线性收敛
Model identification and local linear convergence of coordinate descent
论文作者
论文摘要
对于复合非平滑优化问题，前提算法在有限数量的迭代次数之后实现了模型识别（例如，套索的支持识别），前提是目标函数足够常规。有关坐标下降的结果是稀缺，模型识别仅显示了特定估计器，例如支持矢量机。在这项工作中，我们表明循环坐标下降在有限的时间内实现了模型识别，以实现广泛的功能。此外，我们证明了坐标下降的明确局部线性收敛速率。对各种估计器和实际数据集的广泛实验表明，这些速率与经验结果良好。
For composite nonsmooth optimization problems, Forward-Backward algorithm achieves model identification (e.g. support identification for the Lasso) after a finite number of iterations, provided the objective function is regular enough. Results concerning coordinate descent are scarcer and model identification has only been shown for specific estimators, the support-vector machine for instance. In this work, we show that cyclic coordinate descent achieves model identification in finite time for a wide class of functions. In addition, we prove explicit local linear convergence rates for coordinate descent. Extensive experiments on various estimators and on real datasets demonstrate that these rates match well empirical results.
