Gradient-descent based iterative algorithms pervade a variety of problems in estimation, prediction, learning, control, and optimization. Recently iterative algorithms based on higher-order information have been explored in an attempt to lead to accelerated learning. In this paper, we explore a specific a high-order tuner that has been shown to result in stability with time-varying regressors in linearly parametrized systems, and accelerated convergence with constant regressors. We show that this tuner continues to provide bounded parameter estimates even if the gradients are corrupted by noise. Additionally, we also show that the parameter estimates converge exponentially to a compact set whose size is dependent on noise statistics. As the HT algorithms can be applied to a wide range of problems in estimation, filtering, control, and machine learning, the result obtained in this paper represents an important extension to the topic of real-time and fast decision making.

翻译：基于梯度的基于梯度的迭代算法在估计、预测、学习、控制和优化方面渗透出各种问题。最近根据较高顺序信息的迭代算法已经探索过,试图加速学习。在本文中,我们探索了一种特定的高序调子,显示它与线性对称系统中时间变化的递减器具有稳定性,并加速与不断递减器的趋同。我们表明,即使梯度受到噪音的腐蚀,这个调子仍继续提供受约束的参数估计值。此外,我们还表明,参数估计数指数指数化地汇集到一个依靠噪音统计的紧凑集。由于HT算法可以应用于在估计、过滤、控制和机器学习方面的一系列广泛问题,因此,本文件取得的结果是实时和快速决策主题的重要延伸。