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首页> 外文期刊>IEEE Transactions on Automatic Control >Analysis of Stochastic Approximation Schemes With Set-Valued Maps in the Absence of a Stability Guarantee and Their Stabilization
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Analysis of Stochastic Approximation Schemes With Set-Valued Maps in the Absence of a Stability Guarantee and Their Stabilization

机译：在没有稳定性保证的情况下，在没有稳定性保证的情况下与设定值的随机近似方案分析及其稳定性

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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-mentioned result is an effective instrument for analyzing stochastic approximation schemes in the absence of a stability guarantee, by using it to obtain an alternate criterion 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 Borkar, Andrieu et & x00A0;al., and Chen et & x00A0;al., by allowing for the presence of set-valued drift functions.
机译：在本文中，我们在没有稳定性保证的情况下分析随机映像方案的行为。我们证明，在大量迭代之后，如果随机近似过程进入吸引集的吸引座位，它被锁定到具有高概率的吸引集中。我们证明，上述结果是用于在没有稳定性保证的情况下分析随机近似方案的有效仪器，通过使用它来获得用于平均场的局部吸引的集合的替代标准和通过使用据表明，涉及以规则间隔重置迭代的反馈机制，当平均字段具有全局吸引集时稳定方案，从而保证收敛。这篇论文中的结果构建了<斜体> Borkar，Andrieu et＆x00a0; al。，和<斜体> chen et＆x00a0; al。，通过允许存在 - 偏移漂移功能。

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