  We investigate online convex optimization in changing environments, and
choose the adaptive regret as the performance measure. The goal is to achieve a
small regret over every interval so that the comparator is allowed to change
over time. Different from previous works that only utilize the convexity
condition, this paper further exploits smoothness to improve the adaptive
regret. To this end, we develop novel adaptive algorithms for convex and smooth
functions, and establish problem-dependent regret bounds over any interval. Our
regret bounds are comparable to existing results in the worst case, and become
much tighter when the comparator has a small loss.
