随机截断随机算法的渐近正态性
Asymptotic normality of randomly truncated stochastic algorithms
摘要：
研究了随机截断随机算法的收敛速度，该随机截断随机算法是在一个增紧集序列上截断标准Robbins-Monro过程.在实际中，当标准算法由于期望值函数增长太快而失败时，通常需要这样的截断来确保收敛。在这项工作中，我们在期望值函数的局部假设下给出了该算法的中心极限定理的自包含证明，这些假设在实践中相当容易检验。
英文摘要：
We study the convergence rate of randomly truncated stochastic algorithms, which consist in the truncation of the standard Robbins-Monro procedure on an increasing sequence of compact sets. Such a truncation is often required in practice to ensure convergence when standard algorithms fail because the expected-value function grows too fast. In this work, we give a self contained proof of a central limit theorem for this algorithm under local assumptions on the expected-value function, which are fairly easy to check in practice.
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