AdamW天天用但理论有坑，这篇论文把收敛性列为开放问题，还给出了新分析框架。做LLM训练优化的人该看看。
AdamW是训练大型语言模型的默认优化器，但其理论主要建立在有限方差假设上。实证发现LLM预训练中的随机梯度噪声通常是重尾的。近期Lion、Muon等符号优化器已取得重尾收敛率，AdaGrad也能在重尾噪声下收敛。本文提出一个开放问题：AdamW能否在相同重尾假设下收敛？作者证明了一个正加权度量基准，并通过走廊下界机制表明分母记忆可能隐藏大梯度。
Open Problem: Is AdamW Effective Under Heavy-Tailed Noise?
AdamW is the de facto optimizer for training large language models (LLMs), yet the theory behind it still lives mostly in finite-variance regimes. This is increasingly unsatisfying, as empirical evidence indicates that stochastic gradient noise in LLM pretraining is typically heavy-tailed. Recent work shows that sign-based optimizers such as Lion and Muon achieve sharp heavy-tailed rates, and that AdaGrad can also converge under heavy-tailed noise. However, no rigorous convergence theory for AdamW has yet been established in this regime. Can AdamW converge under the same heavy-tailed assumptions, or does its second-moment accumulator create a genuine obstruction? We formulate this as an open problem, prove a positive weighted-metric benchmark, and give a corridor lower-bound mechanism showing how denominator memory can hide large gradients.