Dynamic regret of convex and smooth functions
WebDynamic Regret of Convex and Smooth Functions. Zhao, Peng. ; Zhang, Yu-Jie. ; Zhang, Lijun. ; Zhou, Zhi-Hua. We investigate online convex optimization in non … 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 gradient descent (OGD) achieves this lower bound using multiple gradient queries per round. In this paper, we focus on unconstrained online optimization.
Dynamic regret of convex and smooth functions
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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 … 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: •
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. 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 …
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. WebJul 7, 2024 · Specifically, we propose novel online algorithms that are capable of leveraging smoothness and replace the dependence on T in the dynamic regret by problem-dependent quantities: the variation in gradients of loss functions, and the cumulative loss of the comparator sequence.
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 …
http://proceedings.mlr.press/v144/zhao21a/zhao21a.pdf#:~:text=To%20minimize%20the%20dynamic%20regret%20of%20strongly%20convex,following%20dynamic%20regret%20ft%28xt%29%20t%3D1%20ft%28x%03t%29%14%20O%28minfPT%3BSTg%29%3A%20%283%29t%3D1 east elementary school bryson city ncWebJun 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. cubix corporationWebthe 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 ... cubix footwearWebWe propose a novel online approach for convex and smooth functions, named Smoothness-aware online learning with dynamic regret (abbreviated as Sword). There are three versions, including Sword var, Sword small, and Sword best. All of them enjoy … east elementary school littleton coloradoWebJul 7, 2024 · Dynamic Regret of Convex and Smooth Functions. We investigate online convex optimization in non-stationary environments and choose the dynamic regret as … east elementary school minden neWebJun 6, 2024 · The regret bound of dynamic online learning algorithms is often expressed in terms of the variation in the function sequence (V_T) and/or the path-length of the … cubix classified searcherWebJun 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 … east elementary school jefferson city