论文标题
无免费午餐定理的重要性是什么？
What is important about the No Free Lunch theorems?
论文作者
论文摘要
无免费的午餐定理证明，在统一的分布中，在诱导问题（搜索问题或学习问题）下，所有诱导算法都同样执行。正如我在本章中讨论的那样，定理的重要性是通过使用它们来分析涉及{非统一}分布的方案，并比较不同的算法，而没有任何关于问题的分布的假设。特别是，定理证明了{anti} -cross-validation（在一组基于{最糟糕的样本外行为）和交叉验证的基于一组候选算法中进行选择，除非一个人做出的假设 - 从未被正式化的一种相互交配的态度，否则在某种程度上进行了cross的分配，而不是在某种程度上进行了cross的分配，而不是在某种程度上进行了cross，那就是在某种程度上进行了cross的分配。验证，另一方面。此外，他们对文献中许多结果的重要性建立了强有力的警告，这些结果在不假设特定分布的情况下确立了特定算法的强度。他们还激励了监督学习和改进黑框优化之间的``字典''，这使人们可以``翻译''技术从监督学习到黑框优化的领域，从而增强了黑盒优化算法。除了这些主题外，我还简要讨论了它们对科学哲学的影响。
The No Free Lunch theorems prove that under a uniform distribution over induction problems (search problems or learning problems), all induction algorithms perform equally. As I discuss in this chapter, the importance of the theorems arises by using them to analyze scenarios involving {non-uniform} distributions, and to compare different algorithms, without any assumption about the distribution over problems at all. In particular, the theorems prove that {anti}-cross-validation (choosing among a set of candidate algorithms based on which has {worst} out-of-sample behavior) performs as well as cross-validation, unless one makes an assumption -- which has never been formalized -- about how the distribution over induction problems, on the one hand, is related to the set of algorithms one is choosing among using (anti-)cross validation, on the other. In addition, they establish strong caveats concerning the significance of the many results in the literature which establish the strength of a particular algorithm without assuming a particular distribution. They also motivate a ``dictionary'' between supervised learning and improve blackbox optimization, which allows one to ``translate'' techniques from supervised learning into the domain of blackbox optimization, thereby strengthening blackbox optimization algorithms. In addition to these topics, I also briefly discuss their implications for philosophy of science.
