Robust loss functions play a critical role in training resilient machine learning models, yet their theoretical foundations remain underexplored. In this talk, I will present my work focused on advancing the theoretical understanding of a wide range of robust loss functions commonly used in risk minimization tasks across various machine learning applications. Specifically, I will try to address the following key questions: (1) What are the primary theoretical challenges in analyzing robust loss functions? (2) How can we understand the robustness of these loss functions? (3) How can we evaluate the out-of-sample generalization performance of models trained using robust loss functions?

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