Lunch Theorem Research Articles

Escaping the No Free Lunch Theorem: A Priori Advantages of Regret-Based Meta-Induction

ABSTRACTA new solution strategy for the problem of induction has been developed based on a priori advantages of regret-weighted meta-induction (RW) in prediction tasks. These a priori advantages seem to contradict the no-free lunch (NFL) theorem. In this paper, the NFL challenge is dissolved by three novel results: (1) RW enjoys free lunches in the long run. (2) Yet, the NFL theorem applies to iterated prediction tasks, because the distribution underlying it assigns a zero probability to all possible worlds in which RW enjoys free lunches. (3) The a priori advantages of RW can even be demonstrated for the short run.

A Meta-analysis on Classification Model Performance in Real-World Datasets: An Exploratory View

ABSTRACTThe No Free Lunch (NFL) Theorem imposes a theoretical restriction on optimization algorithms and their equal average performance on different problems, under some particular assumptions. Nevertheless, when brought into practice, a perceived “ranking” on the performance is usually perceived by engineers developing machine learning applications. Questions that naturally arise are what kinds of biases the real world has and in which ways can we take advantage from them. Using exploratory data analysis (EDA) on classification examples, we gather insight on some traits that set apart algorithms, datasets and evaluation measures and to what extent the NFL theorem, a theoretical result, applies under typical real-world constraints.

Remarks on a recent paper on the "no free lunch" theorems

This note discusses the recent paper Some technical remarks on the proof of the no free lunch by Koppen (2000). In that paper, some technical issues related to the formal proof of the no free lunch (NFL) theorem for search were given by Wolpert and Macready (1995, 1997). The present authors explore the issues raised in that paper including the presentation of a simpler version of the NFL proof in accord with a suggestion made explicitly by Koppen (2000) and implicitly by Wolpert and Macready (1997). They also includes the correction of an incorrect claim made by Koppen (2000) of a limitation of the NFL theorem. Finally, some thoughts on future research directions for research into algorithm performance are given.