具有多值映射的随机近似方案的行为分析及其稳定化（无稳定性保证的情况下）
Analysis of stochastic approximation schemes with set-valued maps in the absence of a stability guarantee and their stabilization
AI总结：
本文分析了在无稳定性保证情况下，具有多值映射的随机近似方案的行为，证明了在吸引集领域内迭代后，方案以高概率被锁定在吸引集内。通过该结果，本文提供了在局部吸引集存在时收敛的替代判据，并展示了当均场具有全局吸引集时，定期重置迭代的反馈机制可稳定方案。
摘要：
在本文中，我们分析了在无稳定性保证情况下，具有多值映射的随机近似方案的行为。我们证明，如果随机近似过程进入吸引集的吸引域，则在大量迭代后，它将以高概率被锁定在吸引集内。我们展示了该结果在无稳定性保证情况下分析随机近似方案的有效性，通过该结果获得均场局部吸引集存在时的收敛替代判据，并通过该结果证明，当均场具有全局吸引集时，定期重置迭代的反馈机制可稳定方案，从而保证收敛。本文的结果基于V.S. Borkar、C. Andrieu和H. F. Chen的工作，允许存在多值漂移函数。
英文摘要：
In this paper, we analyze the behavior of stochastic approximation schemes with set-valued maps in the absence of a stability guarantee. We prove that after a large number of iterations if the stochastic approximation process enters the domain of attraction of an attracting set it gets locked into the attracting set with high probability. We demonstrate that the above result is an effective instrument for analyzing stochastic approximation schemes in the absence of a stability guarantee, by using it obtain an alternate criteria for convergence in the presence of a locally attracting set for the mean field and by using it to show that a feedback mechanism, which involves resetting the iterates at regular time intervals, stabilizes the scheme when the mean field possesses a globally attracting set, thereby guaranteeing convergence. The results in this paper build on the works of V.S. Borkar, C. Andrieu and H. F. Chen , by allowing for the presence of set-valued drift functions.
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