WebDynamic Regret of Convex and Smooth Functions. Zhao, Peng. ; Zhang, Yu-Jie. ; Zhang, Lijun. ; Zhou, Zhi-Hua. We investigate online convex optimization in non … WebWe investigate online convex optimization in non-stationary environments and choose the dynamic regret as the performance measure, defined as the difference between cumulative loss incurred by the online algorithm and that of any feasible comparator sequence.
Improved Analysis for Dynamic Regret of Strongly Convex and Smooth ...
WebJan 24, 2024 · Strongly convex functions are strictly convex, and strictly convex functions are convex. ... The function h is said to be γ-smooth if its gradients are ... as a merit function between the dynamic regret problem and the fixed-point problem, which is reformulation of certain variational inequalities (Facchinei and Pang, 2007). We leave … Webthe dynamic regret R∗ T can be upper bounded by O(p TP∗ T) [Yang et al., 2016]. If all the functions are strongly convex and smooth, the upper bound of R∗ T can be improved to O(P∗ T) [Mokhtari et al., 2016]. The O(P∗ T) rate is also achievable when all the functions are convex and smooth, and all the minimizers x∗ mercer family weekend 2022
Dynamic Regret of Convex and Smooth Functions
Web) small-loss regret bound when the online convex functions are smooth and non-negative, where F T is the cumulative loss of the best decision in hindsight, namely, F T = P T t=1 f … WebJun 10, 2024 · In this paper, we present an improved analysis for dynamic regret of strongly convex and smooth functions. Specifically, we investigate the Online Multiple Gradient Descent (OMGD) algorithm proposed by Zhang et al. (2024). Webthe proximal part is solved approximately. In [1], the following dynamic regret bounds were obtained for the objective functions being smooth and strongly convex: R T = O(1 + T+ P T+ E T); and for the objective functions being smooth and convex: (1.3) R T = O(1 + T+ T+ T+ P T+ P T+ E T); where T = P T k=1 kx k x k 1 k 2. Also, P T = P k=1 k and ... mercer farmers branch