Related papers: Free Lunch for Optimisation under the Universal Di…
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 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 increasing popularity of metaheuristic algorithms has attracted a great deal of attention in algorithm analysis and performance evaluations. No-free-lunch theorems are of both theoretical and practical importance, while many important…
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?…
Challenging optimization problems, which elude acceptable solution via conventional calculus methods, arise commonly in different areas of industrial design and practice. Hard optimization problems are those who manifest the following…
No-Free-Lunch Theorems state, roughly speaking, that the performance of all search algorithms is the same when averaged over all possible objective functions. This fact was precisely formulated for the first time in a now famous paper by…
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…
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…
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…
According to the No Free Lunch (NFL) theorems all black-box algorithms perform equally well when compared over the entire set of optimization problems. An important problem related to NFL is finding a test problem for which a given…
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 ultimate limits for the quantum machine learning of quantum data are investigated by obtaining a generalisation of the celebrated No Free Lunch (NFL) theorem. We find a lower bound on the quantum risk (the probability that a trained…
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…
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 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…
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…
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…
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…
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…