The problem of designing learners that provide guarantees that their predictions are provably correct is of increasing importance in machine learning. However, learning theoretic guarantees have only been considered in very specific settings. In this work, we consider the design and analysis of reliable learners in challenging test-time environments as encountered in modern machine learning problems: namely `adversarial' test-time attacks (in several variations) and `natural' distribution shifts. In this work, we provide a reliable learner with provably optimal guarantees in such settings. We discuss computationally feasible implementations of the learner and further show that our algorithm achieves strong positive performance guarantees on several natural examples: for example, linear separators under log-concave distributions or smooth boundary classifiers under smooth probability distributions.

翻译：在机器学习中，设计能够保证其预测结果可证明正确的学习器这一问题日益重要。然而，学习理论上的保证仅在非常特定的场景中被考虑过。在本研究中，我们探讨了现代机器学习问题中常见的具有挑战性的测试阶段环境下的可靠学习器的设计与分析：即“对抗性”测试阶段攻击（多种变体）和“自然”分布偏移。我们在此类环境中提供了一个具有可证明的最优保证的可靠学习器。我们讨论了该学习器在计算上可行的实现方案，并进一步表明我们的算法在多个自然实例中取得了强劲的正面性能保证：例如，对数凹分布下的线性分类器或光滑概率分布下的光滑边界分类器。