Robust Training in High Dimensions via Block Coordinate Geometric Median Descent

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Publication date: 16 June 2021

Abstract: Geometric median ( extsc{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 extsc{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 extsc{Gm}.

Has companion code repository: https://github.com/anishacharya/Optimization-Mavericks

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