Related papers: What is important about the No Free Lunch theorems…

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…

The no free lunch theorem states that no model is better suited to every problem. A question that arises from this is how to design methods that propose optimizers tailored to specific problems achieving state-of-the-art performance. This…

Machine learning has achieved tremendous success in a variety of domains in recent years. However, a lot of these success stories have been in places where the training and the testing distributions are extremely similar to each other. In…

A critical problem in the field of post hoc explainability is the lack of a common foundational goal among methods. For example, some methods are motivated by function approximation, some by game theoretic notions, and some by obtaining…

Machine learning methods often fail when deployed in the real world. Worse still, they fail in high-stakes situations and across socially sensitive lines. These issues have a chilling effect on the adoption of machine learning methods in…

In learning-assisted theorem proving, one of the most critical challenges is to generalize to theorems unlike those seen at training time. In this paper, we introduce INT, an INequality Theorem proving benchmark, specifically designed to…

The no-free-lunch (NFL) theorem is a celebrated result in learning theory that limits one's ability to learn a function with a training data set. With the recent rise of quantum machine learning, it is natural to ask whether there is a…

Inverse reinforcement learning (IRL) attempts to infer human rewards or preferences from observed behavior. Since human planning systematically deviates from rationality, several approaches have been tried to account for specific human…

Across machine learning (ML) sub-disciplines researchers make mathematical assumptions to facilitate proof-writing. While such assumptions are necessary for providing mathematical guarantees for how algorithms behave, they also necessarily…

In this paper, we prove a crucial theorem called Mirroring Theorem which affirms that given a collection of samples with enough information in it such that it can be classified into classes and subclasses then (i) There exists a mapping…

Cross-validation is a popular non-parametric method for evaluating the accuracy of a predictive rule. The usefulness of cross-validation depends on the task we want to employ it for. In this note, I discuss a simple non-parametric setting,…

We consider the learning of algorithmic tasks by mere observation of input-output pairs. Rather than studying this as a black-box discrete regression problem with no assumption whatsoever on the input-output mapping, we concentrate on tasks…

Evolutionary transfer optimization (ETO) has been gaining popularity in research over the years due to its outstanding knowledge transfer ability to address various challenges in optimization. However, a pressing issue in this field is that…

We show how any PAC learning algorithm that works under the uniform distribution can be transformed, in a blackbox fashion, into one that works under an arbitrary and unknown distribution $\mathcal{D}$. The efficiency of our transformation…

Large Reasoning Models (LRMs) have achieved remarkable performance on complex tasks by engaging in extended reasoning before producing final answers, yet this strength introduces the risk of overthinking, where excessive token generation…

In this overview article we will consider the deliberate restarting of algorithms, a meta technique, in order to improve the algorithm's performance, e.g., convergence rates or approximation guarantees. One of the major advantages is that…

Self-supervised representation learning in computer vision relies heavily on hand-crafted image transformations to learn meaningful and invariant features. However few extensive explorations of the impact of transformation design have been…

The certification of intrinsic randomness is foundational to quantum information theory and central in many practical applications thereof, such as in the generation of unquestionably random numbers and in cryptographic protocols.…

Over the past decade, several researchers have presented various optimisation algorithms for use in truss design. The no free lunch theorem implies that no optimisation algorithm fits all problems; therefore, the interest is not only in the…

Data has now become a shortcoming of deep learning. Researchers in their own fields share the thinking that "deep neural networks might not always perform better when they eat more data," which still lacks experimental validation and a…