BetweenStochasticandAdversarialOnlineConvex Optimization: ImprovedRegretBoundsvia Smoothness

By exploiting smoothness of the expected losses, these bounds replace dependence onthemaximum gradient length bythevariance of the gradients, which was previously known only for linear losses. In addition, theyweakenthei.i.d.assumptionbyallowing,forexample,adversariallypoisoned rounds, which were previously considered in the expert and bandit setting.