We generalized a modified exponentialized estimator by pushing the robust-optimal (RO) index $\lambda$ to $-\infty$ for achieving robustness to outliers by optimizing a quasi-Minimin function. The robustness is realized and controlled adaptively by the RO index without any predefined threshold. Optimality is guaranteed by expansion of the convexity region in the Hessian matrix to largely avoid local optima. Detailed quantitative analysis on both robustness and optimality are provided. The results of proposed experiments on fitting tasks for three noisy non-convex functions and the digits recognition task on the MNIST dataset consolidate the conclusions.

翻译：我们通过将鲁棒-最优（RO）指数$\lambda$推向$-\infty$，优化准极小化函数，推广了一种修正指数化估计器，以实现对异常值的鲁棒性。该鲁棒性通过RO指数自适应地实现和控制，无需任何预定义阈值。通过扩展Hessian矩阵中的凸性区域以大幅避免局部最优，保证了最优性。本文对鲁棒性和最优性均提供了详细的定量分析。针对三个含噪非凸函数的拟合任务以及MNIST数据集上的数字识别任务所提出的实验结果，进一步巩固了相关结论。