We present new algorithms for online convex optimization over unbounded domains that obtain parameter-free regret in high-probability given access only to potentially heavy-tailed subgradient estimates. Previous work in unbounded domains considers only in-expectation results for sub-exponential subgradients. Unlike in the bounded domain case, we cannot rely on straight-forward martingale concentration due to exponentially large iterates produced by the algorithm. We develop new regularization techniques to overcome these problems. Overall, with probability at most $\delta$, for all comparators $\mathbf{u}$ our algorithm achieves regret $\tilde{O}(\| \mathbf{u} \| T^{1/\mathfrak{p}} \log (1/\delta))$ for subgradients with bounded $\mathfrak{p}^{th}$ moments for some $\mathfrak{p} \in (1, 2]$.

翻译：我们提出了在无约束域上实现在线同系物优化的新算法,这些算法在高概率下获得无参数的遗憾,但只能获得潜在的超速子梯度估计值。 在未连接域中, 先前的工作只考虑亚奢侈次梯度的预期结果。 与受约束域例不同, 我们无法依赖由此算法生成的指数性大迭代值的直向式马丁格尔浓度。 我们开发了新的正规化技术来克服这些问题。 总的来说, 对于所有参照国 $\ mathbf{ u} 我们的算法实现了对 $\ tdelde{ O} (\\\\\\\\\ mathbf{u}\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\</s>