非凸优化中随机牛顿方法的收敛性
Convergence of a Randomized Newton Method in Nonconvex Optimization
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中文总结 AI 辅助
本文分析了一种结合牛顿算法与状态相关高斯噪声的随机牛顿方法，用于非凸优化中定位唯一全局极小值点，并证明了有界域下的全局几乎必然收敛性。
中文摘要 AI 辅助
我们分析了一种随机牛顿优化方案，用于定位一般非凸目标函数的唯一全局极小值点。该方法将牛顿算法与具有状态相关方差的可加高斯噪声相结合。在有界域设定下，我们证明了全局几乎必然收敛性。证明基于该算法的两个特性：非退化探索性质，确保在有限步后进入极小值点的邻域；以及噪声衰减性质，以高概率产生收缩并防止无限次离开极小值邻域。
英文摘要
We analyze a stochastic Newton optimization scheme for locating the unique global minimizer of a general nonconvex objective function. The method couples a Newton algorithm to additive Gaussian noise with state-dependent variance. In the bounded domain setting, we prove global almost sure convergence. The proof is based on two features of the algorithm: a nondegenerate exploratory property that ensures entrance into a neighborhood of the minimizer after a finite number of steps, and a decaying-noise property that yields contraction with high probability and prevents infinitely many exits from the neighborhood of the minimum.
