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Workshop: OPT 2022: Optimization for Machine Learning

A Novel Stochastic Gradient Descent Algorithm for LearningPrincipal Subspaces

Charline Le Lan · Joshua Greaves · Jesse Farebrother · Mark Rowland · Fabian Pedregosa · Rishabh Agarwal · Marc Bellemare


In this paper, we derive an algorithm that learns a principal subspace from sample entries, can be applied when the approximate subspace is represented by a neural network, and hence can bescaled to datasets with an effectively infinite number of rows and columns. Our method consistsin defining a loss function whose minimizer is the desired principal subspace, and constructing agradient estimate of this loss whose bias can be controlled.

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