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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…
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…
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…
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…
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 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…
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…
We show how the necessary and sufficient conditions for the NFL to apply can be reduced to the single requirement of the set of objective functions under consideration being closed under permutation, and quantify the extent to which a set…
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 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…
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…
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…
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…
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…
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 gold standard in human-AI collaboration is complementarity -- when combined performance exceeds both the human and algorithm alone. We investigate this challenge in binary classification settings where the goal is to maximize 0-1…
There is no free lunch, no single learning algorithm that will outperform other algorithms on all data. In practice different approaches are tried and the best algorithm selected. An alternative solution is to build new algorithms on demand…
The "No Free Lunch" theorem dictates that no single recommender algorithm is optimal for all users, creating a significant Algorithm Selection Problem. Standard meta-learning approaches aim to solve this by selecting an algorithm based on…