We present an adaptive stochastic variance reduced method with an implicit approach for adaptivity. As a variant of SARAH, our method employs the stochastic recursive gradient yet adjusts step-size based on local geometry. We provide convergence guarantees for finite-sum minimization problems and show a faster convergence than SARAH can be achieved if local geometry permits. Furthermore, we propose a practical, fully adaptive variant, which does not require any knowledge of local geometry and any effort of tuning the hyper-parameters. This algorithm implicitly computes step-size and efficiently estimates local Lipschitz smoothness of stochastic functions. The numerical experiments demonstrate the algorithm's strong performance compared to its classical counterparts and other state-of-the-art first-order methods.

翻译：我们提出了一个适应性随机差异缩小方法,并隐含适应性方法。作为合成孔径雷达的变方,我们的方法采用随机递归梯度,但根据当地几何进行分级调整。我们为有限总和最小化问题提供了趋同保证,并表明如果当地几何允许,可以比合成孔径雷达更快地达到趋同。此外,我们提出了一个实用的、完全适应性变方,它不需要任何当地几何知识和任何调整超参数的努力。这一算法含蓄地计算了逐步规模和高效率地估计当地Libschitz的随机功能的平稳性。数字实验表明算法与其传统的对应方和其他最先进的一级方法相比表现良好。