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The problem of learning threshold functions is a fundamental one in machine learning. Classical learning theory implies sample complexity of $O(\xi^{-1} \log(1/\beta))$ (for generalization error $\xi$ with confidence $1-\beta$). The private…
Partial-label learning is a kind of weakly-supervised learning with inexact labels, where for each training example, we are given a set of candidate labels instead of only one true label. Recently, various approaches on partial-label…
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…
Probably Approximately Correct (i.e., PAC) learning is a core concept of sample complexity theory, and efficient PAC learnability is often seen as a natural counterpart to the class P in classical computational complexity. But while the…
We investigate the connections between the fields of distributed computing and measurable combinatorics by considering complexity classes of locally checkable labeling problems on regular forests. We show that the most important…
The offline reinforcement learning (RL) problem is often motivated by the need to learn data-driven decision policies in financial, legal and healthcare applications. However, the learned policy could retain sensitive information of…
Self-training algorithms, which train a model to fit pseudolabels predicted by another previously-learned model, have been very successful for learning with unlabeled data using neural networks. However, the current theoretical…
We consider online learning problems in the realizable setting, where there is a zero-loss solution, and propose new Differentially Private (DP) algorithms that obtain near-optimal regret bounds. For the problem of online prediction from…
We study the problem of multiclass classification with an extremely large number of classes (k), with the goal of obtaining train and test time complexity logarithmic in the number of classes. We develop top-down tree construction…
We study the problem of estimating mixtures of Gaussians under the constraint of differential privacy (DP). Our main result is that $\text{poly}(k,d,1/\alpha,1/\varepsilon,\log(1/\delta))$ samples are sufficient to estimate a mixture of $k$…
Learning theory has largely focused on two main learning scenarios. The first is the classical statistical setting where instances are drawn i.i.d. from a fixed distribution and the second scenario is the online learning, completely…
We study exact active learning of binary and multiclass classifiers with margin. Given an $n$-point set $X \subset \mathbb{R}^m$, we want to learn any unknown classifier on $X$ whose classes have finite strong convex hull margin, a new…
Partially observable environments present a considerable computational challenge in reinforcement learning due to the need to consider long histories. Learning with a finite window of observations quickly becomes intractable as the window…
Building systems that autonomously create temporal abstractions from data is a key challenge in scaling learning and planning in reinforcement learning. One popular approach for addressing this challenge is the options framework (Sutton et…
In this paper, we prove that Distributional Reinforcement Learning (DistRL), which learns the return distribution, can obtain second-order bounds in both online and offline RL in general settings with function approximation. Second-order…
Despite its empirical success, deep learning still lacks a comprehensive theoretical understanding of model fitting and generalization. This paper proposes the probability distribution (PD) learning framework to analyze the optimization and…
Local differential privacy (LDP) has become a central topic in data privacy research, offering strong privacy guarantees by perturbing user data at the source and removing the need for a trusted curator. However, the noise introduced by LDP…
Recently, the authors introduced the theory of high-arity PAC learning, which is well-suited for learning graphs, hypergraphs and relational structures. In the same initial work, the authors proved a high-arity analogue of the Fundamental…
On-line learning of a rule given by an N-dimensional Ising perceptron, is considered for the case when the student is constrained to take values in a discrete state space of size $L^N$. For L=2 no on-line algorithm can achieve a finite…
The unwavering success of deep learning in the past decade led to the increasing prevalence of deep learning methods in various application fields. However, the downsides of deep learning, most prominently its lack of trustworthiness, may…