Adaptivity of Stochastic Gradient Methods for Nonconvex Optimization
This addresses the gap between theoretical guarantees and practical usability for practitioners in machine learning, though it appears incremental as it builds on prior techniques.
The paper tackles the problem of hyperparameter sensitivity in stochastic gradient methods for nonconvex optimization by proposing the Geometrized SARAH algorithm, which achieves adaptivity to target accuracy and the Polyak-Łojasiewicz constant while matching or outperforming existing convergence rates.
Adaptivity is an important yet under-studied property in modern optimization theory. The gap between the state-of-the-art theory and the current practice is striking in that algorithms with desirable theoretical guarantees typically involve drastically different settings of hyperparameters, such as step-size schemes and batch sizes, in different regimes. Despite the appealing theoretical results, such divisive strategies provide little, if any, insight to practitioners to select algorithms that work broadly without tweaking the hyperparameters. In this work, blending the "geometrization" technique introduced by Lei & Jordan 2016 and the \texttt{SARAH} algorithm of Nguyen et al., 2017, we propose the Geometrized \texttt{SARAH} algorithm for non-convex finite-sum and stochastic optimization. Our algorithm is proved to achieve adaptivity to both the magnitude of the target accuracy and the Polyak-Łojasiewicz (PL) constant if present. In addition, it achieves the best-available convergence rate for non-PL objectives simultaneously while outperforming existing algorithms for PL objectives.