论文标题
低复杂性正规化器的迭代正则化
Iterative regularization for low complexity regularizers
论文作者
论文摘要
迭代正则化利用了优化算法的隐式偏差，以使不适当的问题正常。使用这种内置正规化机制构建算法是反问题的经典挑战，也是现代机器学习，它既提供了算法分析的新观点，又提供了与显式正则化相比的大幅加速。在这项工作中，我们提出和研究了第一个迭代正则化程序，能够处理由非平滑和非强凸功能描述的偏差，这在低复杂性正则化中很突出。我们的方法基于一种原始的二算法，即使在原始问题是不可行的情况下，我们也可以分析收敛性和稳定性。考虑到$ \ ell_1 $罚款的稀疏恢复的特殊情况。我们的理论结果通过实验显示了我们方法的计算益处。
Iterative regularization exploits the implicit bias of an optimization algorithm to regularize ill-posed problems. Constructing algorithms with such built-in regularization mechanisms is a classic challenge in inverse problems but also in modern machine learning, where it provides both a new perspective on algorithms analysis, and significant speed-ups compared to explicit regularization. In this work, we propose and study the first iterative regularization procedure able to handle biases described by non smooth and non strongly convex functionals, prominent in low-complexity regularization. Our approach is based on a primal-dual algorithm of which we analyze convergence and stability properties, even in the case where the original problem is unfeasible. The general results are illustrated considering the special case of sparse recovery with the $\ell_1$ penalty. Our theoretical results are complemented by experiments showing the computational benefits of our approach.
