AI-SARAH: Adaptive and Implicit Stochastic Recursive Gradient Methods

• URL: http://arxiv.org/abs/2102.09700v1
• Date: Fri, 19 Feb 2021 01:17:15 GMT
• Title: AI-SARAH: Adaptive and Implicit Stochastic Recursive Gradient Methods
• Authors: Zheng Shi and Nicolas Loizou and Peter Richt\'arik and Martin Tak\'a\v{c}
• Abstract summary: We present an adaptive variance reduced method with an implicit approach for adaptivity. We provide convergence guarantees for finite-sum minimization problems and show a faster convergence than SARAH can be achieved if local geometry permits. This algorithm implicitly computes step-size and efficiently estimates local Lipschitz smoothness of functions.
• Score: 7.486132958737807
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

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