Smoothness Assumption

The "smoothness assumption" in machine learning and related fields refers to the degree to which a function or data distribution varies locally. Current research focuses on relaxing traditional smoothness assumptions, exploring alternatives like $(L_0, L_1)$-smoothness, and developing algorithms (e.g., AdaGrad, Adam, and variants of gradient descent) that perform well under weaker conditions. This is crucial because many real-world problems, particularly in deep learning and federated learning, violate strong smoothness requirements. Improved understanding and handling of smoothness assumptions lead to more robust and efficient algorithms for various applications, including image processing, generative modeling, and optimization problems in general.