13 accepted papers
We study the task of online learning in the presence of Massart noise. Specifically, instead of assuming that the online adversary chooses an arbitrary sequence of labels, we assume that the context $\boldsymbol{x}$ is selected adversarially but the label $y$ presented to the learner disagrees wit…
We consider the basic problem of learning Single-Index Models with respect to the square loss under the Gaussian distribution in the presence of adversarial label noise. Our main contribution is the first computationally efficient algorithm for this learning task, achieving a constant factor a…
We study the problem of PAC learning $\gamma$-margin halfspaces in the presence of Massart noise. Without computational considerations, the sample complexity of this learning problem is known to be $\widetilde{\Theta}(1/(\gamma^2 \epsilon))$. Prior computationally efficient algorithms for the pro…
We study the problem of PAC learning halfspaces in the reliable agnostic model of Kalai et al. (2012). The reliable PAC model captures learning scenarios where one type of error is costlier than the others. Our main positive result is a new algorithm for reliable learning of Gaussian halfspace…
We study the problem of learning Single-Index Models under the $L_2^2$ loss in the agnostic model. We give an efficient learning algorithm, achieving a constant factor approximation to the optimal loss, that succeeds under a range of distributions (including log-concave distributions) and a broad cl…
A single-index model (SIM) is a function of the form $\sigma(\mathbf{w}^{\ast} \cdot \mathbf{x})$, where $\sigma: \mathbb{R} \to \mathbb{R}$ is a known link function and $\mathbf{w}^{\ast}$ is a hidden unit vector. We study the task of learning SIMs in the agnostic (a.k.a. adversarial label noise)…
We give the first polynomial-time algorithm for the testable learning of halfspaces in the presence of adversarial label noise under the Gaussian distribution. In the recently introduced testable learning model, one is required to produce a tester-learner such that if the data passes the tester, t…
We study the problem of learning general (i.e., not necessarily homogeneous) halfspaces with Random Classification Noise under the Gaussian distribution. We establish nearly-matching algorithmic and Statistical Query (SQ) lower bound results revealing a surprising information-computation gap for…
We study the problem of learning a single neuron with respect to the $L_2^2$-loss in the presence of adversarial label noise. We give an efficient algorithm that, for a broad family of activations including ReLUs, approximates the optimal $L_2^2$-error within a constant factor. Notably, our algorith…
We study the problem of learning general {—} i.e., not necessarily homogeneous {—} halfspaces with adversarial label noise under the Gaussian distribution. Prior work has provided a sophisticated polynomial-time algorithm for this problem. In this work, we show that the problem can be solved directl…
We study the problem of designing online algorithms given advice about the input. While prior work had focused on deterministic advice, we only assume distributional access to the instances of interest, and the goal is to learn a competitive algorithm given access to i.i.d. samples. We aim to be com…
We study the fundamental problems of agnostically learning halfspaces and ReLUs under Gaussian marginals. In the former problem, given labeled examples $(\bx, y)$ from an unknown distribution on $\R^d \times \{ \pm 1\}$, whose marginal distribution on $\bx$ is the standard Gaussian and the labels…
We study the problem of agnostically learning homogeneous halfspaces in the distribution-specific PAC model. For a broad family of structured distributions, including log-concave distributions, we show that non-convex SGD efficiently converges to a solution with misclassification error $O(\opt)+\e…