Dynamic Regret of Online Mirror Descent for Relatively Smooth Convex Cost Functions

The performance of online convex optimization algorithms in a dynamic environment is often expressed terms the regret, which measures decision maker’s against sequence time-varying comparators. In analysis prior works assume Lipschitz continuity or uniform smoothness cost functions. However, there are many important functions practice that do not satisfy these conditions. such cases, analyses applicable and fail to guarantee performance. this letter, we show it possible bound even when neither nor present. We adopt notion relative with respect some user-defined regularization function, much milder requirement on first under smoothness, regret has an upper based path length functional variation. then additional condition relatively strong convexity, can be bounded by gradient These bounds provide guarantees wide variety problems arise different application domains. Finally, present numerical experiments demonstrate advantage adopting function smooth.