Recently, several universal methods have been proposed for online convex optimization which can handle convex, strongly convex and exponentially concave cost functions simultaneously. However, most of these algorithms have been designed with static regret minimization in mind, but this notion of regret may not be suitable for changing environments. To address this shortcoming, we propose a novel and intuitive framework for universal online optimization in dynamic environments. Unlike existing universal algorithms, our strategy does not rely on the construction of a set of experts and an accompanying meta-algorithm. Instead, we show that the problem of dynamic online optimization can be reduced to a uniclass prediction problem. By leaving the choice of uniclass loss function in the user's hands, they are able to control and optimize dynamic regret bounds, which in turn carry over into the original problem. To the best of our knowledge, this is the first paper proposing a universal approach with state-of-the-art dynamic regret guarantees even for general convex cost functions.

翻译：近期，针对在线凸优化问题已提出多种通用方法，可同时处理凸函数、强凸函数和指数凹代价函数。然而，这些算法大多基于静态遗憾最小化设计，该遗憾概念可能不适用于动态环境。为弥补此缺陷，我们提出一种新颖且直观的动态环境通用在线优化框架。与现有通用算法不同，本策略无需构建专家集及配套元算法，而是证明动态在线优化问题可归约为单类预测问题。通过让用户自主选择单类损失函数，可控制并优化动态遗憾界，该界值将自然传递至原问题。据我们所知，这是首篇提出通用方法的研究，即便对一般凸代价函数也能实现最先进的动态遗憾保证。