Abstract: Geometric median (GM) is a classical method in statistics for achieving robust estimation of the uncorrupted data; under gross corruption, it achieves the optimal breakdown point of 1/2. However, its computational complexity makes it infeasible for robustifying stochastic gradient descent (SGD) in high-dimensional optimization problems. In this paper, we show that by applying GM to only a judiciously chosen block of coordinates at a time and using a memory mechanism, one can retain the breakdown point of 1/2 for smooth non-convex problems, with non-asymptotic convergence rates comparable to the SGD with GM while resulting in significant speedup in training. We further validate the run-time and robustness of our approach empirically on several popular deep learning tasks. Code available at: https://github.com/anishacharya/BGMD
- Coordinate Descent
- Deep Learning
- High-Dimensional Statistics
- Robust Learning
- Stochastic Gradient Methods
Download: arXiv version, slides, poster, code
- Robust Training in High Dimensions via Block Coordinate Geometric Median Descent (arXiv, slides, poster, code)
A. Acharya, A. Hashemi, P. Jain, S. Sanghavi, I. Dhillon, U. Topcu.
In International Conference on Artificial Intelligence and Statistics (AISTATS), March 2022.