这篇论文提出了HT-PAder算法，不用提前知道任何参数就能在重尾噪声下做动态优化，比以往方法更通用，理论结果也很强。
该论文针对重尾噪声下的非平稳在线凸优化问题，其中随机梯度仅存在有限p阶中心矩(p∈(1,2])。研究者提出HT-PAder算法，通过结合重启AdaGrad专家和路径元算法AdaGrad-Hedge实现参数无关的通用动态遗憾。HT-PAder在直径D、Lipschitz常数G、噪声水平σ和比较器路径长度P_T下达到期望遗憾界Õ(GD√(T(1+P_T/D)) + σD T^{1/p}(1+P_T/D)^{(p-1)/p})，无需任何先验参数知识。即使p=2时，这也是首个无参数极小极大通用动态遗憾保证，并证明了匹配的下界。
Parameter-Free Dynamic Regret for Online Convex Optimization under Heavy-Tailed Noise
We study online convex optimization (OCO) in non-stationary environments under heavy-tailed noise, where the stochastic gradient oracle admits only a finite $p$-th central moment for some $p \in (1, 2]$. While static regret is well-understood, achieving universal dynamic regret in a parameter-free manner remains an open challenge. We resolve this by proposing \textbf{HT-PAder}, a parameter-free algorithm combining restarted AdaGrad experts over a geometric pool of block lengths with a pathwise meta-algorithm, \textbf{AdaGrad-Hedge}, which requires no moment conditions on meta-losses. For a domain of diameter $D$, Lipschitz constant $G$, noise level $σ$, and comparator path length $P_T$, HT-PAder achieves an expected universal dynamic regret of \[ \widetilde O\left( GD\sqrt{T(1+P_T/D)} + σD T^{1/p}(1+P_T/D)^{(p-1)/p} \right). \] The algorithm does not require prior knowledge of any of these problem parameters. Even in the special case of finite variance ($p=2$), HT-PAder provides the first parameter-free minimax universal dynamic regret guarantee. We also prove a matching lower bound, establishing the optimality of the path-length exponent.