  Adaptive gradient methods such as Adam have gained extreme popularity due to
their success in training complex neural networks and less sensitivity to
hyperparameter tuning compared to SGD. However, it has been recently shown that
Adam can fail to converge and might cause poor generalization -- this lead to
the design of new, sophisticated adaptive methods which attempt to generalize
well while being theoretically reliable. In this technical report we focus on
AdaBound, a promising, recently proposed optimizer. We present a stochastic
convex problem for which AdaBound can provably take arbitrarily long to
converge in terms of a factor which is not accounted for in the convergence
rate guarantee of Luo et al. (2019). We present a new $O(\sqrt T)$ regret
guarantee under different assumptions on the bound functions, and provide
empirical results on CIFAR suggesting that a specific form of momentum SGD can
match AdaBound's performance while having less hyperparameters and lower
computational costs.
