  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.
