Stochastic and Adversarial Online Learning without Hyperparameters

Most online optimization algorithms focus on one of two things: performing well in adversarial settings by adapting to unknown data parameters (such as Lipschitz constants), typically achieving O( T) regret, or performing well in stochastic settings where they can leverage some structure in the losses (such as strong convexity), typically achieving O(log(T)) regret. Algorithms that focus on the former problem hitherto achieved O( T) in the stochastic setting rather than O(log(T)).