Title: Enhancing Machine Learning Generalization Through Distributional Robustness

Abstract: In modern machine learning, generalization beyond observed training data remains a fundamental challenge, particularly in the presence of distribution shifts. Distributionally Robust Learning (DRL) offers a principled approach to addressing this challenge by optimizing for worst-case scenarios within a specified uncertainty set. In this talk, I will present two of our recent works tha leverage DRL to enhance adaptation and generalization. The first work, Gradual Domain Adaptation via Manifold-Constrained Distributionally Robus Optimization, introduces a novel DRL-based framework incorporating manifold constraints to facilitate smooth adaptation across a sequence of shifting domains. This approach ensures stability and improves model robustness in real-world scenarios where data distributions evolve gradually over time. The second work, Out-Of-Domain Unlabeled Data Improves Generalization, challenges the conventional reliance on in-domain data for model training. It is shown that strategically incorporating out-of-domain, unlabeled data under a DRL framework can significantly enhanc performance, even in previously unseen environments. By integrating robust optimization principles, these approaches provide new insights into improving machine learning models in dynamic and uncertain settings. Theoretical foundations, methodological innovations, and empirical results will be discussed to highlight the effectiveness of DRL in addressing real-world challenges.