Can Adaptive Gradient Methods Converge under Heavy-Tailed Noise? A Case Study of AdaGrad
Why popular AI optimizers work even when math predicts they should fail
AdaGrad, a foundational algorithm used in machine learning optimization, can successfully navigate noisy training environments where extreme outlier values occur—without needing extra safeguards like gradient clipping that other methods require. This finding applies when the noise follows heavy-tailed distributions and the algorithm automatically adapts to the severity of the problem without advance warning.
Popular optimizers like Adam and AdamW are built on AdaGrad's principles, so understanding why AdaGrad works under chaotic, noisy training conditions explains why these widely-used tools perform reliably in practice. This closes a gap between theory and practice: machine learning practitioners have long observed these algorithms working well on messy real-world tasks, but the math didn't fully explain why until now.