论文标题
对抗反应的普遍回归
Universal Regression with Adversarial Responses
论文作者
论文摘要
我们为回归提供了算法，并在大型非i.i.d类中具有对抗反应。实例序列，在一般可分开的度量空间上，其假设最少。在这种回归环境中，我们还提供了可学习性的特征。我们考虑普遍的一致性，该一致性要求学习者的强大一致性，而无需限制价值响应。我们的分析表明，对于一个比静态过程要大得多的实例序列可以实现的目标，并且揭示了价值空间之间的基本二分法：有限 - 霍森是否平均估计是可以实现的。我们进一步提供了乐观的通用学习规则，即，如果它们无法实现普遍的一致性，那么任何其他算法也将失败。对于无限的损失，我们提出了一种轻度的集成性条件，在该条件下存在算法，用于在大型非i.i.d类中进行对抗回归的算法。实例序列。此外，我们的分析还为一般度量空间中的平均值估计提供了一个学习规则，该规则在对抗反应下是一致的，而无需任何时刻条件，这是独立利益的结果。
We provide algorithms for regression with adversarial responses under large classes of non-i.i.d. instance sequences, on general separable metric spaces, with provably minimal assumptions. We also give characterizations of learnability in this regression context. We consider universal consistency which asks for strong consistency of a learner without restrictions on the value responses. Our analysis shows that such an objective is achievable for a significantly larger class of instance sequences than stationary processes, and unveils a fundamental dichotomy between value spaces: whether finite-horizon mean estimation is achievable or not. We further provide optimistically universal learning rules, i.e., such that if they fail to achieve universal consistency, any other algorithms will fail as well. For unbounded losses, we propose a mild integrability condition under which there exist algorithms for adversarial regression under large classes of non-i.i.d. instance sequences. In addition, our analysis also provides a learning rule for mean estimation in general metric spaces that is consistent under adversarial responses without any moment conditions on the sequence, a result of independent interest.
