We present an effective framework for improving the breakdown point of robust regression algorithms. Robust regression has attracted widespread attention due to the ubiquity of outliers, which significantly affect the estimation results. However, many existing robust least-squares regression algorithms suffer from a low breakdown point, as they become stuck around local optima when facing severe attacks. By expanding on the previous work, we propose a novel framework that enhances the breakdown point of these algorithms by inserting a prior distribution in each iteration step, and adjusting the prior distribution according to historical information. We apply this framework to a specific algorithm and derive the consistent robust regression algorithm with iterative local search (CORALS). The relationship between CORALS and momentum gradient descent is described, and a detailed proof of the theoretical convergence of CORALS is presented. Finally, we demonstrate that the breakdown point of CORALS is indeed higher than that of the algorithm from which it is derived. We apply the proposed framework to other robust algorithms, and show that the improved algorithms achieve better results than the original algorithms, indicating the effectiveness of the proposed framework.

翻译：我们提出了一种有效提升鲁棒回归算法崩溃点的框架。由于异常值普遍存在且显著影响估计结果，鲁棒回归已引起广泛关注。然而，现有许多鲁棒最小二乘回归算法存在崩溃点较低的问题——面对严重攻击时易陷入局部最优。在先前工作的基础上，我们提出一种新型框架，通过在每个迭代步骤中插入先验分布，并依据历史信息调整该先验分布，从而提升算法的崩溃点。我们将此框架应用于特定算法，推导出具有迭代局部搜索的一致性鲁棒回归算法（CORALS）。阐述了CORALS与动量梯度下降法的关联，并提供了CORALS理论收敛性的详细证明。最后证明了CORALS的崩溃点确实高于其派生算法。将该框架应用于其他鲁棒算法后，改进算法均取得优于原始算法的表现，充分验证了所提框架的有效性。