论文标题
随机方差降低了仿射等级最小化问题的梯度
Stochastic Variance Reduced Gradient for affine rank minimization problem
论文作者
论文摘要
我们开发有效的随机方差降低了梯度下降算法，以解决仿射等级最小化问题包括从线性测量中找到最低等级的基质。所提出的作为随机梯度下降策略的算法比完整的梯度更为有利。它还降低了每次迭代时随机梯度的方差，并加速了收敛速度。我们证明，在有限的等轴测情况下，提出的算法在溶液中线性收敛。数值实验表明，与其他最先进的贪婪算法相比，所提出的算法效率，适应性和准确性具有明显有利的平衡。
We develop an efficient stochastic variance reduced gradient descent algorithm to solve the affine rank minimization problem consists of finding a matrix of minimum rank from linear measurements. The proposed algorithm as a stochastic gradient descent strategy enjoys a more favorable complexity than full gradients. It also reduces the variance of the stochastic gradient at each iteration and accelerate the rate of convergence. We prove that the proposed algorithm converges linearly in expectation to the solution under a restricted isometry condition. The numerical experiments show that the proposed algorithm has a clearly advantageous balance of efficiency, adaptivity, and accuracy compared with other state-of-the-art greedy algorithms.
