Related papers: On the equivalence of Occam algorithms

We extend the theory of PAC learning in a way which allows to model a rich variety of learning tasks where the data satisfy special properties that ease the learning process. For example, tasks where the distance of the data from the…

In a recent article, Alon, Hanneke, Holzman, and Moran (FOCS '21) introduced a unifying framework to study the learnability of classes of partial concepts. One of the central questions studied in their work is whether the learnability of a…

We compute that the index set of PAC-learnable concept classes is $m$-complete $\Sigma^0_3$ within the set of indices for all concept classes of a reasonable form. All concept classes considered are computable enumerations of computable…

This paper is about the recent notion of computably probably approximately correct learning, which lies between the statistical learning theory where there is no computational requirement on the learner and efficient PAC where the learner…

We revisit the problem of characterising the complexity of Quantum PAC learning, as introduced by Bshouty and Jackson [SIAM J. Comput. 1998, 28, 1136-1153]. Several quantum advantages have been demonstrated in this setting, however, none…

We study the collaborative PAC learning problem recently proposed in Blum et al.~\cite{BHPQ17}, in which we have $k$ players and they want to learn a target function collaboratively, such that the learned function approximates the target…

We present a formal proof in Lean of probably approximately correct (PAC) learnability of the concept class of decision stumps. This classic result in machine learning theory derives a bound on error probabilities for a simple type of…

The standard definition of PAC learning (Valiant 1984) requires learners to succeed under all distributions -- even ones that are intractable to sample from. This stands in contrast to samplable PAC learning (Blum, Furst, Kearns, and Lipton…

We study computable PAC (CPAC) learning as introduced by Agarwal et al. (2020). First, we consider the main open question of finding characterizations of proper and improper CPAC learning. We give a characterization of a closely related…

In this paper we study the problem of multiclass classification with a bounded number of different labels $k$, in the realizable setting. We extend the traditional PAC model to a) distribution-dependent learning rates, and b) learning rates…

Much of learning theory is concerned with the design and analysis of probably approximately correct (PAC) learners. The closely related transductive model of learning has recently seen more scrutiny, with its learners often used as…

A fundamental result of statistical learnig theory states that a concept class is PAC learnable if and only if it is a uniform Glivenko-Cantelli class if and only if the VC dimension of the class is finite. However, the theorem is only…

We consider quantum versions of two well-studied classical learning models: Angluin's model of exact learning from membership queries and Valiant's Probably Approximately Correct (PAC) model of learning from random examples. We give…

In the problem of learning with label proportions, which we call LLP learning, the training data is unlabeled, and only the proportions of examples receiving each label are given. The goal is to learn a hypothesis that predicts the…

The empirical risk minimization (ERM) principle has been highly impactful in machine learning, leading both to near-optimal theoretical guarantees for ERM-based learning algorithms as well as driving many of the recent empirical successes…

Motivated by results on generic-case complexity in group theory, we apply the ideas of effective Baire category and effective measure theory to study complexity classes of functions which are "fractionally computable" by a partial…

We study a recent model of collaborative PAC learning where $k$ players with $k$ different tasks collaborate to learn a single classifier that works for all tasks. Previous work showed that when there is a classifier that has very small…

Machine learning researchers and practitioners steadily enlarge the multitude of successful learning models. They achieve this through in-depth theoretical analyses and experiential heuristics. However, there is no known general-purpose…

The basic problem in the PAC model of computational learning theory is to determine which hypothesis classes are efficiently learnable. There is presently a dearth of results showing hardness of learning problems. Moreover, the existing…

We continue the study of the computational complexity of differentially private PAC learning and how it is situated within the foundations of machine learning. A recent line of work uncovered a qualitative equivalence between the private…