Related papers: No-Free-Lunch Theorems in the continuum
The No Free Lunch (NFL) theorem for search and optimisation states that averaged across all possible objective functions on a fixed search space, all search algorithms perform equally well. Several refined versions of the theorem find a…
Function optimisation is a major challenge in computer science. The No Free Lunch theorems state that if all functions with the same histogram are assumed to be equally probable then no algorithm outperforms any other in expectation. We…
Stemming from a paper of Auger and Teytaud, there is a common misconception that for continuous domains No Free Lunch (NFL) does not hold. However, Rowe, Vose, and Wright have demonstrated that NFL holds for arbitrary domains and…
The sharpened No-Free-Lunch-theorem (NFL-theorem) states that the performance of all optimization algorithms averaged over any finite set F of functions is equal if and only if F is closed under permutation (c.u.p.) and each target function…
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…
The no-free-lunch theorems promote a skeptical conclusion that all possible machine learning algorithms equally lack justification. But how could this leave room for a learning theory, that shows that some algorithms are better than others?…
The No Free Lunch theorems are often used to argue that domain specific knowledge is required to design successful algorithms. We use algorithmic information theory to argue the case for a universal bias allowing an algorithm to succeed in…
No free lunch theorems for supervised learning state that no learner can solve all problems or that all learners achieve exactly the same accuracy on average over a uniform distribution on learning problems. Accordingly, these theorems are…
The No Free Lunch (NFL) theorem guarantees equal average performance only under uniform sampling of a function space closed under permutation (c.u.p.). We ask when this averaging ceases to reflect what benchmarking actually reports. We…
This paper is concerned with learners who aim to learn patterns in infinite binary sequences: shown longer and longer initial segments of a binary sequence, they either attempt to predict whether the next bit will be a 0 or will be a 1 or…
The important recent book by G. Schurz appreciates that the no-free-lunch theorems (NFL) have major implications for the problem of (meta) induction. Here I review the NFL theorems, emphasizing that they do not only concern the case where…
Multitask learning and related areas such as multi-source domain adaptation address modern settings where datasets from $N$ related distributions $\{P_t\}$ are to be combined towards improving performance on any single such distribution…
The concept of absence of opportunities for free lunches is one of the pillars in the economic theory of financial markets. This natural assumption has proved very fruitful and has lead to great mathematical, as well as economical, insights…
Tensor network machine learning models have shown remarkable versatility in tackling complex data-driven tasks, ranging from quantum many-body problems to classical pattern recognitions. Despite their promising performance, a comprehensive…
In a recent paper it was shown that No Free Lunch results hold for any subset F of the set of all possible functions from a finite set X to a finite set Y iff F is closed under permutation of X. In this article, we prove that the number of…
The Free Lunch Principle: Nature thrives on freebies. She chooses nothing, and no one helps Her. She must use canonical mathematical structures as there is no one to tell Her otherwise. With this I show where variational principles are…
The main result of the paper is a version of the fundamental theorem of asset pricing (FTAP) for large financial markets based on an asymptotic concept of no market free lunch for monotone concave preferences. The proof uses methods from…
The rapid advancement of machine learning techniques has re-energized research into general artificial intelligence. While the idea of domain-agnostic meta-learning is appealing, this emerging field must come to terms with its relationship…
No-regret learning dynamics ensure that a learner asymptotically achieves an average reward no worse than that of any fixed strategy. This no-regret guarantee does not determine the value of the asymptotic average reward. Indeed, it is…
We show that there exists an entire function which has neither fixed points nor invariant Baker domains. The question whether such a function exists was raised by Buff.