site stats

Dynamic regret of convex and smooth functions

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. WebFor strongly convex and smooth functions, Zhang et al. (2024) establish the squared path-length of the minimizer sequence (C*_ {2,T}) as a lower bound on regret. They also show that online gradient descent (OGD) achieves this lower bound using multiple gradient queries per round. In this paper, we focus on unconstrained online optimization.

Peng Zhao [email protected] …

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). WebJun 10, 2024 · When multiple gradients are accessible to the learner, we first demonstrate that the dynamic regret of strongly convex functions can be upper bounded by the … calculating consumer and producer surplus https://digiest-media.com

Dynamic Regret of Online Mirror Descent for Relatively …

WebMulti-Object Manipulation via Object-Centric Neural Scattering Functions ... Dynamic Aggregated Network for Gait Recognition ... Improving Generalization with Domain Convex Game Fangrui Lv · Jian Liang · Shuang Li · Jinming Zhang · Di Liu SLACK: Stable Learning of Augmentations with Cold-start and KL regularization ... 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 … WebApr 26, 2024 · of every interval [r, s] ⊆ [T].Requiring a low regret over any interval essentially means the online learner is evaluated against a changing comparator. For convex functions, the state-of-the-art algorithm achieves an O (√ (s − r) log s) regret over any interval [r, s] (Jun et al., 2024), which is close to the minimax regret over a fixed … calculating concrete in yards

Dynamic Regret of Convex and Smooth Functions

Category:Improved Analysis for Dynamic Regret of Strongly Convex and …

Tags:Dynamic regret of convex and smooth functions

Dynamic regret of convex and smooth functions

arXiv:2304.04710v1 [math.OC] 10 Apr 2024

http://www.lamda.nju.edu.cn/zhaop/publication/NeurIPS

Dynamic regret of convex and smooth functions

Did you know?

WebAlthough this bound is proved to be minimax optimal for convex functions, in this paper, we demonstrate that it is possible to further enhance the dynamic regret by exploiting the … 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 t(x) with x chosen as the o ine minimizer. The key ingredient in the analysis is to exploit the self-bounding properties of smooth functions.

WebJul 7, 2024 · Abstract. We investigate online convex optimization in non-stationary environments and choose the dynamic regret as the performance measure, defined as the difference between cumulative loss ... 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∗

http://www.lamda.nju.edu.cn/zhaop/publication/arXiv_Sword.pdf WebJun 6, 2024 · For strongly convex and smooth functions, , Zhang et al. establish the squared path-length of the minimizer sequence ($C^*_ {2,T}$) as a lower bound on regret. They also show that online...

WebApr 26, 2024 · 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...

WebFeb 28, 2024 · The performance of online convex optimization algorithms in a dynamic environment is often expressed in terms of the dynamic regret, which measures the … coach and horses kew bridgeWebWe propose a novel online approach for convex and smooth functions, named Smoothness-aware online learning with dynamic regret (abbreviated as Sword). There … calculating contribution margin ratioWebApr 10, 2024 · on the dynamic regret of the algorithm when the regular part of the cost is convex and smooth. If the Bregman distance is given by the Euclidean distance, our result also im- calculating corrected serum sodiumWebFeb 28, 2024 · We first show that under relative smoothness, the dynamic regret has an upper bound based on the path length and functional variation. We then show that with an additional condition of relatively strong convexity, the dynamic regret can be bounded by the path length and gradient variation. calculating corrected qt intervalhttp://www.lamda.nju.edu.cn/zhaop/publication/arXiv_Sword.pdf coach and horses llangynidr websitehttp://proceedings.mlr.press/v97/zhang19j/zhang19j.pdf calculating corporate income taxWebthe 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 ... coach and horses horsley village