提出首个鲁棒学习单调广义线性模型的多项式算法
Robustly Learning Monotone Generalized Linear Models via Data Augmentation
- 通过渐减高斯噪声数据增强，实现对任意单调激活函数的鲁棒学习
- 首次在任意单调利普希茨激活下达到常数因子近似，适用于所有有界(2+ζ)阶矩的激活函数
- 解决长期开放问题，适合关注鲁棒统计学习与理论机器学习的研究者
我们研究在高斯分布下的异构模型中学习广义线性模型（GLMs）的任务。首次提出一个多项式时间算法，对任意单调利普希茨激活函数均能实现常数因子近似。此前的常数因子GLM学习器仅适用于更小的激活函数类。本工作解决了长期存在的公开问题，开发出经典GLMtron算法（Kakade等, 2011）的鲁棒版本。所提鲁棒学习器适用范围更广，涵盖所有具有有界(2+ζ)阶矩（ζ>0为任意固定值）的单调激活函数——这一条件几乎是必要的。为获得结果，我们引入一种新颖的数据增强技术：逐步减小的高斯噪声注入，并证明了若干结构性结论，可能在其他场景中也有应用价值。
原文摘要 · Abstract (English)
We study the task of learning Generalized Linear models (GLMs) in the agnostic model under the Gaussian distribution. We give the first polynomial-time algorithm that achieves a constant-factor approximation for \textit{any} monotone Lipschitz activation. Prior constant-factor GLM learners succeed for a substantially smaller class of activations. Our work resolves a well-known open problem, by developing a robust counterpart to the classical GLMtron algorithm (Kakade et al., 2011). Our robust learner applies more generally, encompassing all monotone activations with bounded $(2+ζ)$-moments, for any fixed $ζ>0$ -- a condition that is essentially necessary. To obtain our results, we leverage a novel data augmentation technique with decreasing Gaussian noise injection and prove a number of structural results that may be useful in other settings.
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