Dynamic regret of convex and smooth functions

Author: dyrl

August undefined, 2024

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. Let T be the time horizon and PT be the path-length that essentially reflects the non-stationarity of … 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 minimum of the path-length and the ...

Dynamic Regret of Convex and Smooth Functions

WebFeb 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. WebBesbes, Gur, and Zeevi (2015) show that the dynamic regret can be bounded by O(T2 =3(V T + 1) 1) and O(p T(1 + V T)) for convex functions and strongly convex … ciol find a translator

Dynamic regret of convex and smooth functions Proceedings …

WebJul 7, 2024 · Dynamic Regret of Convex and Smooth Functions. We investigate online convex optimization in non-stationary environments and choose the dynamic regret as … 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. WebTg) dynamic regret.Yang et al.(2016) disclose that the O(P T) rate is also attainable for convex and smooth functions, provided that all the minimizers x t’s lie in the interior of the feasible set X. Besides,Besbes et al.(2015) show that OGD with a restarting strategy attains an O(T2=3V1=3 T) dynamic regret when the function variation V ciolina bouw

Adaptive Regret of Convex and Smooth Functions DeepAI

Dynamic Regret of Convex and Smooth Functions - NASA/ADS

http://proceedings.mlr.press/v97/zhang19j/zhang19j.pdf WebApr 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- cio - lewis structureWebJun 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 gradient descent (OGD) achieves this lower bound using multiple gradient queries per round. In this paper, we focus on unconstrained online optimization. dialog\\u0027s of

"Webdynamic regret of convex cost functions [3], [10], [11], which can be improved to O(p TC T) when prior knowledge of C and T is available [12]. The path length has also been recently used in the study of online convex optimization with constraint violation [13], where upper bounds of O(p T(1+C T)) and O(p T) are derived on the dynamic regret and ... " - Dynamic regret of convex and smooth functions

Dynamic regret of convex and smooth functions

The optimal dynamic regret for smoothed online convex …

Webthe function is strongly convex, the dependence on din the upper bound disappears (Zhang et al., 2024b). For convex functions, Hazan et al. (2007) modify the FLH algorithm by replacing the expert-algorithm with any low-regret method for convex functions, and introducing a para-meter of step size in the meta-algorithm. In this case, the efﬁ- WebJun 10, 2024 · 06/10/20 - In this paper, we present an improved analysis for dynamic regret of strongly convex and smooth functions. Specifically, we invest...

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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 … 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 … WebWe investigate online convex optimization in non-stationary environments and choose the dynamic regret as the performance measure, defined as the difference between …

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∗

WebJul 7, 2024 · Dynamic Regret of Convex and Smooth Functions. We investigate online convex optimization in non-stationary environments and choose the dynamic regret as … dialog\\u0027s thWebT) 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 = PT t=1 ft(x ∗) with x∗ chosen as the oﬄine minimizer. The key ingredient in the analysis is to exploit the self-bounding properties of smooth functions. ciol find a linguistWebFor 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. dialogue about bias and prejudiceWebApr 1, 2024 · By applying the SOGD and OMGD algorithms for generally convex or strongly-convex and smooth loss functions, we obtain the optimal dynamic regret, which matches the theoretical lower bound. In seeking to achieve the optimal regret for OCO l 2 SC, our major contributions can be summarized as follows: • dialog\\u0027s whWebJun 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 … dialogue about learning computerWebApr 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 … dialogue about fake newsWebDynamic Regret of Convex and Smooth Functions. Zhao, Peng. ; Zhang, Yu-Jie. ; Zhang, Lijun. ; Zhou, Zhi-Hua. We investigate online convex optimization in non … c iom