Related papers: From average case complexity to improper learning …
The goal of a learning algorithm is to receive a training data set as input and provide a hypothesis that can generalize to all possible data points from a domain set. The hypothesis is chosen from hypothesis classes with potentially…
We prove hardness-of-learning results under a well-studied assumption on the existence of local pseudorandom generators. As we show, this assumption allows us to surpass the current state of the art, and prove hardness of various basic…
Adversarially robust PAC learning has proved to be challenging, with the currently best known learners [Montasser et al., 2021a] relying on improper methods based on intricate compression schemes, resulting in sample complexity exponential…
As learning solutions reach critical applications in social, industrial, and medical domains, the need to curtail their behavior has become paramount. There is now ample evidence that without explicit tailoring, learning can lead to biased,…
Using the recently developed framework of [Daniely et al, 2014], we show that under a natural assumption on the complexity of refuting random K-SAT formulas, learning DNF formulas is hard. Furthermore, the same assumption implies the…
We study the complexity of PAC learning halfspaces in the presence of Massart noise. In this problem, we are given i.i.d. labeled examples $(\mathbf{x}, y) \in \mathbb{R}^N \times \{ \pm 1\}$, where the distribution of $\mathbf{x}$ is…
We study the computational complexity of adversarially robust proper learning of halfspaces in the distribution-independent agnostic PAC model, with a focus on $L_p$ perturbations. We give a computationally efficient learning algorithm and…
In this paper, we consider the problem of replicable realizable PAC learning. We construct a particularly hard learning problem and show a sample complexity lower bound with a close to $(\log|H|)^{3/2}$ dependence on the size of the…
We show strong (and surprisingly simple) lower bounds for weakly learning intersections of halfspaces in the improper setting. Strikingly little is known about this problem. For instance, it is not even known if there is a polynomial-time…
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…
A central question in computer science and statistics is whether efficient algorithms can achieve the information-theoretic limits of statistical problems. Many computational-statistical tradeoffs have been shown under average-case…
A fundamental problem in adversarial machine learning is to quantify how much training data is needed in the presence of evasion attacks. In this paper we address this issue within the framework of PAC learning, focusing on the class of…
We show hardness of improperly learning halfspaces in the agnostic model, both in the distribution-independent as well as the distribution-specific setting, based on the assumption that worst-case lattice problems, such as GapSVP or SIVP,…
We prove that it is NP-hard to properly PAC learn decision trees with queries, resolving a longstanding open problem in learning theory (Bshouty 1993; Guijarro-Lavin-Raghavan 1999; Mehta-Raghavan 2002; Feldman 2016). While there has been a…
We study the problem of reducing adversarially robust learning to standard PAC learning, i.e. the complexity of learning adversarially robust predictors using access to only a black-box non-robust learner. We give a reduction that can…
We study the problem of agnostically learning halfspaces which is defined by a fixed but unknown distribution $\mathcal{D}$ on $\mathbb{Q}^n\times \{\pm 1\}$. We define $\mathrm{Err}_{\mathrm{HALF}}(\mathcal{D})$ as the least error of a…
Proper learning refers to the setting in which learners must emit predictors in the underlying hypothesis class $H$, and often leads to learners with simple algorithmic forms (e.g. empirical risk minimization (ERM), structural risk…
A supervised learning algorithm has access to a distribution of labeled examples, and needs to return a function (hypothesis) that correctly labels the examples. The hypothesis of the learner is taken from some fixed class of functions…
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…
Continual learning, or lifelong learning, is a formidable current challenge to machine learning. It requires the learner to solve a sequence of $k$ different learning tasks, one after the other, while retaining its aptitude for earlier…