Average Smoothness

Average smoothness, a measure of a function's effective smoothness relative to an underlying distribution, is a burgeoning research area aiming to improve the efficiency and generalization of machine learning models and algorithms. Current research focuses on establishing theoretical bounds for average smoothness in various settings (e.g., regression, reinforcement learning), developing algorithms that leverage this concept (e.g., stochastic proximal point methods, modified WENO schemes), and applying it to diverse applications including image processing, speech recognition, and medical image analysis. Understanding and exploiting average smoothness offers significant potential for enhancing the performance and robustness of machine learning models across numerous fields.