  We provide a new theoretical analysis framework to investigate online
gradient descent in the dynamic environment. Comparing with the previous work,
the new framework recovers the state-of-the-art dynamic regret, but does not
require extra gradient queries for every iteration. Specifically, when
functions are $\alpha$ strongly convex and $\beta$ smooth, to achieve the
state-of-the-art dynamic regret, the previous work requires $O(\kappa)$ with
$\kappa = \frac{\beta}{\alpha}$ queries of gradients at every iteration. But,
our framework shows that the query complexity can be improved to be $O(1)$,
which does not depend on $\kappa$. The improvement is significant for
ill-conditioned problems because that their objective function usually has a
large $\kappa$.
