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arXiv 2011.04803cs.LG

Self-Tuning Stochastic Optimization with Curvature-Aware Gradient Filtering

University of Toronto(多伦多大学);Vector Institute(向量学院);Max Planck Institute for Intelligent Systems(马克斯·普朗克智能系统研究所)

Ricky T. Q. Chen, Dami Choi, Lukas Balles, David Duvenaud, Philipp Hennig

英文摘要:

Standard first-order stochastic optimization algorithms base their updates solely on the average mini-batch gradient, and it has been shown that tracking additional quantities such as the curvature can help de-sensitize common hyperparameters. Based on this intuition, we explore the use of exact per-sample Hessian-vector products and gradients to construct optimizers that are self-tuning and hyperparameter-free. Based on a dynamics model of the gradient, we derive a process which leads to a curvature-corrected, noise-adaptive online gradient estimate. The smoothness of our updates makes it more amenable to simple step size selection schemes, which we also base off of our estimates quantities. We prove that our model-based procedure converges in the noisy quadratic setting. Though we do not see similar gains in deep learning tasks, we can match the performance of well-tuned optimizers and ultimately, this is an interesting step for constructing self-tuning optimizers.

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