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math.OC2022★ 2 cited
Trajectory of Mini-Batch Momentum: Batch Size Saturation and Convergence in High Dimensions
Kiwon Lee, Andrew N. Cheng, Courtney Paquette +1
We analyze the dynamics of large batch stochastic gradient descent with momentum (SGD+M) on the least squares problem when both the number of samples and dimensions are large. In t…
math.OC2022
Flatness of the nuclear norm sphere, simultaneous polarization, and uniqueness in nuclear norm minimization
Tim Hoheisel, Elliot Paquette
In this paper we establish necessary and sufficient conditions for the existence of line segments (or flats) in the sphere of the nuclear norm via the notion of simultaneous polari…