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.

本文研究了不同的向量步长自适应方法，旨在解决在线、连续预测问题中的非平稳性，提出了一种适用于更广泛算法的基于元梯度下降的增量式自适应步长算法AdaGain，并通过对比发现这种元梯度下降方法在非平稳预测问题中具有优势。

在线、持续预测的元下降法