Online Convex Optimization with Unconstrained Domains and Losses
Online Convex Optimization with Unconstrained Domains and Losses
复制标题
具有无约束域和损失的在线凸优化
DOI：
10.48550/arxiv.2203.10327
复制
发表时间：
2017
期刊：
影响因子：
--
通讯作者：
K. Boahen
中科院分区：
文献类型：
--
作者：
Ashok Cutkosky;K. Boahen
我们提出一种在线凸优化算法（RescaledExp），该算法在无约束设定下能在事先不了解损失函数任何边界的情况下实现最优遗憾值。我们证明了一个下界，它表明了那些需要已知损失函数边界的现有算法的遗憾值与任何不需要此类知识的算法之间存在指数级差距。RescaledExp在迭代次数上渐近地匹配这个下界。RescaledExp自然是无超参数的，并且我们通过实验证明它与那些需要超参数优化的先前的优化算法表现相当。
We propose an online convex optimization algorithm (RescaledExp) that achieves optimal regret in the unconstrained setting without prior knowledge of any bounds on the loss functions. We prove a lower bound showing an exponential separation between the regret of existing algorithms that require a known bound on the loss functions and any algorithm that does not require such knowledge. RescaledExp matches this lower bound asymptotically in the number of iterations. RescaledExp is naturally hyperparameter-free and we demonstrate empirically that it matches prior optimization algorithms that require hyperparameter optimization.