论文标题
高尾巴的高概率无参数后悔
Parameter-free Regret in High Probability with Heavy Tails
论文作者
论文摘要
我们为在线凸出域上提供了新的算法，以优化无界域，这些算法仅访问潜在的重尾亚级别估计值，以获得无参数的遗憾。在无界域中的先前工作仅考虑亚指数亚级别的未观察结果。与有限域的情况不同，由于算法产生的指数较大的迭代，我们不能依靠直接向前的Martingale浓度。我们开发了新的正规化技术来克服这些问题。总体而言，对于所有比较器，最多可能有$δ$，我们的算法就遗憾$ \ tilde {o} {o}（\ | \ | \ | \ Mathbf { $ \ mathfrak {p}^{th} $ moments $ \ mathfrak {p} \ in（1，2] $。
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 $δ$, for all comparators $\mathbf{u}$ our algorithm achieves regret $\tilde{O}(\| \mathbf{u} \| T^{1/\mathfrak{p}} \log (1/δ))$ for subgradients with bounded $\mathfrak{p}^{th}$ moments for some $\mathfrak{p} \in (1, 2]$.
