置信域半径依赖于概率模型的随机置信域方法
Stochastic Trust Region Methods with Trust Region Radius Depending on Probabilistic Models
摘要：
我们提出了一个随机信赖域模型为基础的框架，其半径相关的概率模型。特别是，我们提出了一个特定的算法，称为STRME，其中的信赖域半径线性依赖于最新的模型梯度。分析了非凸、凸和强凸情形下的STRME算法的复杂性，与现有的基于概率性质的算法相匹配。此外，通过数值实验，与已有的随机信赖域方法和其他相关的随机梯度法进行了比较.
英文摘要：
We present a stochastic trust-region model-based framework in which its radius is related to the probabilistic models. Especially, we propose a specific algorithm, termed STRME, in which the trust-region radius depends linearly on the latest model gradient. The complexity of STRME method in non-convex, convex and strongly convex settings has all been analyzed, which matches the existing algorithms based on probabilistic properties. In addition, several numerical experiments are carried out to reveal the benefits of the proposed methods compared to the existing stochastic trust-region methods and other relevant stochastic gradient methods.
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