Dynamic regret of convex and smooth functions
WebApr 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: • 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 …
Dynamic regret of convex and smooth functions
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WebJun 6, 2024 · The regret bound of dynamic online learning algorithms is often expressed in terms of the variation in the function sequence () and/or the path-length of the minimizer sequence after rounds. For strongly convex and smooth functions, , Zhang et al. establish the squared path-length of the minimizer sequence () as a lower bound on regret. 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.
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. 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...
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 … 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 ...
WebReview 1. Summary and Contributions: This paper provides algorithms for online convex optimization with smooth non-negative losses that achieve dynamic regret sqrt( P^2 + …
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 ... chs feed tagsWebT) 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. chs feed productsWebJul 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 ... chs feeds montanaWebthe 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- describing a spooky forestWebFeb 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 … chs feed store bellingham waWebWe 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 … chs feed store everson waWebWe investigate online convex optimization in non-stationary environments and choose the dynamic regret as the performance measure, defined as the difference between … chs feed store kasson mn