In this paper, we address tracking of a time-varying parameter with unknown
dynamics. We formalize the problem as an instance of online optimization in a
dynamic setting. Using online gradient descent, we propose a method that
sequentially predicts the value of the parameter and in turn suffers a loss.
The objective is to minimize the accumulation of losses over the time horizon,
a notion that is termed dynamic regret. While existing methods focus on convex
loss functions, we consider strongly convex functions so as to provide better
guarantees of performance. We derive a regret bound that captures the
path-length of the time-varying parameter, defined in terms of the distance
between its consecutive values. In other words, the bound represents the
natural connection of tracking quality to the rate of change of the parameter.
We provide numerical experiments to complement our theoretical findings.

本文提出一种基于在线梯度下降方法的动态调参算法，以降低动态遗憾（dynamic regret），进而优化强凸且未知动力学的损失函数。