Before revision:  Our main algorithm AdaAGD+ is an accelerated method, which is universal in the sense that it achieves nearly-optimal convergence rates for both smooth and non-smooth functions, even when it only has access to stochastic gradients.
After revision:  Our main algorithms AdaACSA and AdaAGD+ is an accelerated method, which is universal in the sense that it achieves nearly-optimal convergence rates for both smooth and non-smooth functions, even when it only has access to stochastic gradients.