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arXiv · 2106.08882

Robust Training in High Dimensions via Block Coordinate Geometric Median Descent

Anish Acharya·Abolfazl Hashemi·Prateek Jain·Sujay Sanghavi·Inderjit S. Dhillon·Ufuk Topcu
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Abstract

Geometric median (\textsc{Gm}) is a classical method in statistics for achieving a robust estimation of the uncorrupted data; under gross corruption, it achieves the optimal breakdown point of 0.5. However, its computational complexity makes it infeasible for robustifying stochastic gradient descent (SGD) for high-dimensional optimization problems. In this paper, we show that by applying \textsc{Gm} to only a judiciously chosen block of coordinates at a time and using a memory mechanism, one can retain the breakdown point of 0.5 for smooth non-convex problems, with non-asymptotic convergence rates comparable to the SGD with \textsc{Gm}.

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Anish Acharya, Abolfazl Hashemi, Prateek Jain, Sujay Sanghavi, Inderjit S. Dhillon, Ufuk Topcu. 2021-06-16. Robust Training in High Dimensions via Block Coordinate Geometric Median Descent. https://arxiv.org/abs/2106.08882

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