用随机方向估计海森矩阵，降低优化误差，提升收敛速度。
Generalized Random Direction Newton Algorithms for Stochastic Optimization
- 基于噪声函数值构造广义海森估计算法，可调测量次数控制偏差阶数。
- 证明了估计算法渐近无偏，且新牛顿方法具有渐近与非渐近收敛性。
- 适合需要高精度优化的强化学习、黑箱优化场景，尤其关注噪声数据问题。
我们提出一类基于随机方向随机逼近（RDSA）的广义海森估计算法，仅依赖于带有噪声的函数值测量。每个估计算法的形式及其偏差阶数取决于函数测量次数。特别地，我们证明测量次数越多，估计偏差阶数越低。我们证明了这些估计算法的渐近无偏性，并对引入该类海森估计器的随机牛顿方法进行了渐近与非渐近收敛性分析。最后，通过数值实验验证了理论结果的正确性。
原文摘要 · Abstract (English)
We present a family of generalized Hessian estimators of the objective using random direction stochastic approximation (RDSA) by utilizing only noisy function measurements. The form of each estimator and the order of the bias depend on the number of function measurements. In particular, we demonstrate that estimators with more function measurements exhibit lower-order estimation bias. We show the asymptotic unbiasedness of the estimators. We also perform asymptotic and non-asymptotic convergence analyses for stochastic Newton methods that incorporate our generalized Hessian estimators. Finally, we perform numerical experiments to validate our theoretical findings.
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