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Recently, several universal methods have been proposed for online convexoptimization which can handle convex, strongly convex and exponentially concavecost functions simultaneously. However, most of these algorithms have beendesigned with static regret minimization in mind, but this notion of regret maynot be suitable for changing environments. To address this shortcoming, wepropose a novel and intuitive framework for universal online optimization indynamic environments. Unlike existing universal algorithms, our strategy doesnot rely on the construction of a set of experts and an accompanyingmeta-algorithm. Instead, we show that the problem of dynamic onlineoptimization can be reduced to a uniclass prediction problem. By leaving thechoice of uniclass loss function in the user's hands, they are able to controland optimize dynamic regret bounds, which in turn carry over into the originalproblem. To the best of our knowledge, this is the first paper proposing auniversal approach with state-of-the-art dynamic regret guarantees even forgeneral convex cost functions.

Universal Online Optimization in Dynamic Environments via Uniclass Prediction