Universal Online Optimization in Dynamic Environments via Uniclass Prediction

Abstract: 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.