Heavy Tailed Noise

Heavy-tailed noise, characterized by infrequent but extremely large deviations from the mean, poses significant challenges to many machine learning algorithms. Current research focuses on developing robust optimization methods, such as clipped stochastic gradient descent and median-of-means estimators, to mitigate the adverse effects of this noise in various settings, including federated learning and generative models. These advancements are crucial for improving the reliability and efficiency of machine learning systems operating in real-world environments where heavy-tailed noise is prevalent, impacting applications from data analysis to reinforcement learning. The development of high-probability convergence bounds under heavy-tailed assumptions is a key area of ongoing investigation.