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Nov, 2012
次梯度法与条件梯度法之间的对偶性
Duality between subgradient and conditional gradient methods
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Francis Bach
TL;DR
本研究证明了镜面下降算法和条件梯度法广义化算法的等价性，并说明了在某些问题中，如具有非平滑损失或非平滑正则化器的监督式机器学习问题中，原始次梯度法和对偶条件梯度法是形式上等价的；对偶解释导致了镜面下降的线性搜索形式以及对原始-对偶证书的收敛性的保证。
Abstract
In this paper, we show the equivalence between
mirror descent algorithms
and algorithms generalizing the
conditional gradient method
. This is done through convex duality, and implies notably that for certain prob
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