Stochastic Gradient Descent on Riemannian Manifolds
Stochastic Gradient Descent on Riemannian Manifolds
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DOI：
10.1109/tac.2013.2254619
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发表时间：
2013-09-01
影响因子：
6.8
通讯作者：
Bonnabel, Silvere
中科院分区：
文献类型：
--
作者：
Bonnabel, Silvere
随机梯度下降是一种简单的方法，可以找到其评估被噪声破坏的成本函数的局部最小值。在本文中，我们开发了一个程序扩展随机梯度下降算法的情况下，函数定义在黎曼流形。我们证明，在欧几里得的情况下，梯度下降算法收敛到一个临界点的成本函数。该算法有许多潜在的应用，并在这里说明了四个例子。特别是一种新的八卦算法的协方差矩阵的集合推导和数值测试。
Stochastic gradient descent is a simple approach to find the local minima of a cost function whose evaluations are corrupted by noise. In this paper, we develop a procedure extending stochastic gradient descent algorithms to the case where the function is defined on a Riemannian manifold. We prove that, as in the Euclidian case, the gradient descent algorithm converges to a critical point of the cost function. The algorithm has numerous potential applications, and is illustrated here by four examples. In particular a novel gossip algorithm on the set of covariance matrices is derived and tested numerically.