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arXiv · 2311.14387

Achieving Margin Maximization Exponentially Fast via Progressive Norm Rescaling

Mingze Wang·Zeping Min·Lei Wu
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Abstract

In this work, we investigate the margin-maximization bias exhibited by gradient-based algorithms in classifying linearly separable data. We present an in-depth analysis of the specific properties of the velocity field associated with (normalized) gradients, focusing on their role in margin maximization. Inspired by this analysis, we propose a novel algorithm called Progressive Rescaling Gradient Descent (PRGD) and show that PRGD can maximize the margin at an {\em exponential rate}. This stands in stark contrast to all existing algorithms, which maximize the margin at a slow {\em polynomial rate}. Specifically, we identify mild conditions on data distribution under which existing algorithms such as gradient descent (GD) and normalized gradient descent (NGD) {\em provably fail} in maximizing the margin efficiently. To validate our theoretical findings, we present both synthetic and real-world experiments. Notably, PRGD also shows promise in enhancing the generalization performance when applied to linearly non-separable datasets and deep neural networks.

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Mingze Wang, Zeping Min, Lei Wu. 2023-11-24. Achieving Margin Maximization Exponentially Fast via Progressive Norm Rescaling. https://arxiv.org/abs/2311.14387

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