Accelerated Optimization in the PDE Framework Formulations for the Active Contour Case.
Accelerated Optimization in the PDE Framework Formulations for the Active Contour Case.
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DOI：
10.1137/19m1304210
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发表时间：
2020
影响因子：
2.1
通讯作者：
Benyamin M
中科院分区：
文献类型：
--
作者：
Yezzi A;Sundaramoorthi G;Benyamin M
继Nesterov的开创性工作之后，加速优化方法已被用于在二阶优化策略不适用或不切实际的情况下，有力地提高基于梯度的一阶参数估计的性能。加速梯度下降不仅比传统梯度下降收敛得快得多，而且它还通过最初的超调，然后在最终配置中振荡回来，对参数空间进行更鲁棒的局部搜索，从而只选择具有足够大的吸引力基础的局部最小值，以包含初始超调。这种行为使得加速和随机梯度搜索方法在机器学习社区中特别流行。Wibisono、Wilson和Jordan在他们最近发表的2016年PNAS论文《优化加速方法的变分视角》中，展示了如何将一类广泛的加速方案放在围绕Bregman散度制定的变分框架中，从而导致连续体极限ode。我们展示了它们的公式如何进一步扩展到无限维流形（从曲线和曲面的几何空间开始），方法是用切空间上的内积代替Bregman散度，并明确地引入一个分布质量模型，该模型在优化过程中与感兴趣的对象一起发展。引入共进化质量模型纯粹是为了赋予优化以有用的动力学，它还将基于PDE的加速优化方案与最优质量传递的流体动力学公式联系起来。
Following the seminal work of Nesterov, accelerated optimization methods have been used to powerfully boost the performance of first-order, gradient based parameter estimation in scenarios where second-order optimization strategies are either inapplicable or impractical. Not only does accelerated gradient descent converge considerably faster than traditional gradient descent, but it also performs a more robust local search of the parameter space by initially overshooting and then oscillating back as it settles into a final configuration, thereby selecting only local minimizers with a basis of attraction large enough to contain the initial overshoot. This behavior has made accelerated and stochastic gradient search methods particularly popular within the machine learning community. In their recent PNAS 2016 paper, A Variational Perspective on Accelerated Methods in Optimization, Wibisono, Wilson, and Jordan demonstrate how a broad class of accelerated schemes can be cast in a variational framework formulated around the Bregman divergence, leading to continuum limit ODEs. We show how their formulation may be further extended to infinite dimensional manifolds (starting here with the geometric space of curves and surfaces) by substituting the Bregman divergence with inner products on the tangent space and explicitly introducing a distributed mass model which evolves in conjunction with the object of interest during the optimization process. The coevolving mass model, which is introduced purely for the sake of endowing the optimization with helpful dynamics, also links the resulting class of accelerated PDE based optimization schemes to fluid dynamical formulations of optimal mass transport.
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影响因子：
10.6
作者：
Chan, TF;Vese, LA
通讯作者：
Vese, LA
DOI：
10.1109/tpami.2011.150
发表时间：
2012-03-01
影响因子：
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作者：
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通讯作者：
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影响因子：
2.5
作者：
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通讯作者：
Yezzi, A