平方损失学习：通过补偿拉德马赫复杂度的定位
Learning with Square Loss: Localization through Offset Rademacher Complexity
摘要：
我们考虑回归平方损失和一般类的功能没有有界性假设。我们引入了一个概念的偏移拉德马赫复杂度，提供了一个透明的方式来研究本地化的期望和高概率。对于任何（可能是非凸的）类，两步估计的超额损失被证明是通过一个新的几何不等式的偏移复杂性的上界。在凸的情况下，估计减少到经验风险最小化。该方法恢复的结果\citep{RakSriTsy15}的有界的情况下，同时也提供保证，没有有界性假设。
英文摘要：
We consider regression with square loss and general classes of functions without the boundedness assumption. We introduce a notion of offset Rademacher complexity that provides a transparent way to study localization both in expectation and in high probability. For any (possibly non-convex) class, the excess loss of a two-step estimator is shown to be upper bounded by this offset complexity through a novel geometric inequality. In the convex case, the estimator reduces to an empirical risk minimizer. The method recovers the results of \citep{RakSriTsy15} for the bounded case while also providing guarantees without the boundedness assumption.
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