Adaptive Regret of Convex and Smooth Functions
This work addresses the problem of adapting to non-stationary environments in online learning for researchers and practitioners, but it is incremental as it builds on prior methods by incorporating smoothness.
The paper tackles online convex optimization in changing environments by exploiting smoothness to improve adaptive regret, achieving regret bounds that are comparable to existing results in worst-case scenarios and significantly tighter when the comparator has small loss.
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.