  This paper investigates different vector step-size adaptation approaches for
non-stationary online, continual prediction problems. Vanilla stochastic
gradient descent can be considerably improved by scaling the update with a
vector of appropriately chosen step-sizes. Many methods, including AdaGrad,
RMSProp, and AMSGrad, keep statistics about the learning process to approximate
a second order update---a vector approximation of the inverse Hessian. Another
family of approaches use meta-gradient descent to adapt the step-size
parameters to minimize prediction error. These meta-descent strategies are
promising for non-stationary problems, but have not been as extensively
explored as quasi-second order methods. We first derive a general, incremental
meta-descent algorithm, called AdaGain, designed to be applicable to a much
broader range of algorithms, including those with semi-gradient updates or even
those with accelerations, such as RMSProp. We provide an empirical comparison
of methods from both families. We conclude that methods from both families can
perform well, but in non-stationary prediction problems the meta-descent
methods exhibit advantages. Our method is particularly robust across several
prediction problems, and is competitive with the state-of-the-art method on a
large-scale, time-series prediction problem on real data from a mobile robot.
