Parameter-Free Dynamic Regret under Heavy-Tailed Noise

We study online convex optimization with stochastic gradient noise whose conditional $p$-th central moment is bounded by $σ^p$, for an unknown $p\in(1,2]$. For losses with Lipschitz bound $G$ on a domain of diameter $D$, we obtain expected universal dynamic regret $\widetilde O(GD\sqrt{TΛ}+σDT^{1/p}