最优化是应用数学的一个分支,主要指在一定条件限制下,选取某种研究方案使目标达到最优的一种方法。最优化问题在当今的军事、工程、管理等领域有着极其广泛的应用。

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我们提出并分析了一种基于动量的梯度方法,用于训练具有指数尾损失(例如,指数或logistic损失)的线性分类器,它以O (1/t2)的速率最大化可分离数据的分类边缘。这与标准梯度下降的速率O(1/log(t))和标准化梯度下降的速率O(1/t)形成对比。这种基于动量的方法是通过最大边际问题的凸对偶,特别是通过将Nesterov加速度应用于这种对偶,从而在原函数中得到了一种简单而直观的方法。这种对偶观点也可以用来推导随机变量,通过对偶变量进行自适应非均匀抽样。

https://www.zhuanzhi.ai/paper/9fd848dc95d2b0a9a5da37dbbd79d4ed

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This letter addresses the 3D coverage path planning (CPP) problem for terrain reconstruction of unknown obstacle rich environments. Due to sensing limitations, the proposed method, called CT-CPP, performs layered scanning of the 3D region to collect terrain data, where the traveling sequence is optimized using the concept of a coverage tree (CT) with a TSP-inspired tree traversal strategy. The CT-CPP method is validated on a high-fidelity underwater simulator and the results are compared to an existing terrain following CPP method. The results show that CT-CPP yields significant reduction in trajectory length, energy consumption, and reconstruction error.

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