后悔
序列(生物学)
数学
路径(计算)
上下界
凸优化
组合数学
树篱
功能(生物学)
正多边形
数学优化
计算机科学
统计
数学分析
生态学
遗传学
几何学
进化生物学
生物
程序设计语言
作者
Qing-xin Meng,Jian-wei Liu
标识
DOI:10.1016/j.ins.2023.119862
摘要
This work focuses on dynamic regret for non-stationary online convex optimization with full information. State-of-the-art analysis shows that Implicit Online Mirror Descent (IOMD) combined with Hedge achieves an O˜(min{VT,(1+PT)T}) dynamic regret, where VT denotes the temporal variability of the loss functions and PT measures the path length reflecting the non-stationarity of the comparator sequence, and Optimistic IOMD (OptIOMD) enjoys the dynamic regret of O(min{VT′,(1+P)T}), where VT′ denotes the cumulative distance from the loss functions to an arbitrary predictor sequence, and P is an upper bound of the path-length PT. In order to further suppress dynamic regret, we propose an algorithm named Hedge-OptIOMD, which achieves an O˜(min{minj∈1:nVTj,(1+PT)T}) dynamic regret via multiple predictors, where VTj represents the cumulative distance from the loss functions to the j-th predictor sequence. We also verify the advantages of Hedge-OptIOMD through numerical experiments.
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