  In this paper, we study adaptive online convex optimization, and aim to
design a universal algorithm that achieves optimal regret bounds for multiple
common types of loss functions. Existing universal methods are limited in the
sense that they are optimal for only a subclass of loss functions. To address
this limitation, we propose a novel online method, namely Maler, which enjoys
the optimal $O(\sqrt{T})$, $O(d\log T)$ and $O(\log T)$ regret bounds for
general convex, exponentially concave, and strongly convex functions
respectively. The essential idea is to run multiple types of learning
algorithms with different learning rates in parallel, and utilize a meta
algorithm to track the best one on the fly. Empirical results demonstrate the
effectiveness of our method.
