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This paper studies the fundamental limits of reinforcement learning (RL) in the challenging \emph{partially observable} setting. While it is well-established that learning in Partially Observable Markov Decision Processes (POMDPs) requires…

Machine Learning · Computer Science 2023-02-03 Fan Chen , Huan Wang , Caiming Xiong , Song Mei , Yu Bai

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…

Machine Learning · Computer Science 2020-06-15 Ilias Diakonikolas , Vasilis Kontonis , Christos Tzamos , Nikos Zarifis

We study the problem of {\em distribution-independent} PAC learning of halfspaces in the presence of Massart noise. Specifically, we are given a set of labeled examples $(\mathbf{x}, y)$ drawn from a distribution $\mathcal{D}$ on…

Machine Learning · Computer Science 2019-12-11 Ilias Diakonikolas , Themis Gouleakis , Christos Tzamos

We give tight statistical query (SQ) lower bounds for learnining halfspaces in the presence of Massart noise. In particular, suppose that all labels are corrupted with probability at most $\eta$. We show that for arbitrary $\eta \in…

Machine Learning · Computer Science 2022-01-25 Rajai Nasser , Stefan Tiegel

We study efficient PAC learning of homogeneous halfspaces in $\mathbb{R}^d$ in the presence of malicious noise of Valiant (1985). This is a challenging noise model and only until recently has near-optimal noise tolerance bound been…

Machine Learning · Computer Science 2021-10-06 Jie Shen

The increased availability of data in recent years has led several authors to ask whether it is possible to use data as a {\em computational} resource. That is, if more data is available, beyond the sample complexity limit, is it possible…

Machine Learning · Computer Science 2013-11-12 Amit Daniely , Nati Linial , Shai Shalev Shwartz

We study several questions in the reliable agnostic learning framework of Kalai et al. (2009), which captures learning tasks in which one type of error is costlier than others. A positive reliable classifier is one that makes no false…

Machine Learning · Computer Science 2014-02-25 Varun Kanade , Justin Thaler

We study the problem of agnostic learning under the Gaussian distribution. We develop a method for finding hard families of examples for a wide class of problems by using LP duality. For Boolean-valued concept classes, we show that the…

Machine Learning · Computer Science 2021-02-09 Ilias Diakonikolas , Daniel M. Kane , Thanasis Pittas , Nikos Zarifis

Multi-distribution learning extends agnostic Probably Approximately Correct (PAC) learning to the setting in which a family of $k$ distributions, $\{D_i\}_{i\in[k]}$, is considered and a classifier's performance is measured by its error…

Machine Learning · Computer Science 2025-06-24 Chicheng Zhang , Yihan Zhou

The complexity of learning a concept class under Gaussian marginals in the difficult agnostic model is closely related to its $L_1$-approximability by low-degree polynomials. For any concept class with Gaussian surface area at most…

Machine Learning · Computer Science 2026-03-09 Lucas Pesenti , Lucas Slot , Manuel Wiedmer

In the classic point location problem, one is given an arbitrary dataset $X \subset \mathbb{R}^d$ of $n$ points with query access to an unknown halfspace $f : \mathbb{R}^d \to \{0,1\}$, and the goal is to learn the label of every point in…

Data Structures and Algorithms · Computer Science 2025-09-26 Hadley Black , Kasper Green Larsen , Arya Mazumdar , Barna Saha , Geelon So

We study the problem of learning a binary classifier on the vertices of a graph. In particular, we consider classifiers given by monophonic halfspaces, partitions of the vertices that are convex in a certain abstract sense. Monophonic…

Machine Learning · Computer Science 2024-06-19 Marco Bressan , Emmanuel Esposito , Maximilian Thiessen

Our main result is a reduction from worst-case lattice problems such as GapSVP and SIVP to a certain learning problem. This learning problem is a natural extension of the `learning from parity with error' problem to higher moduli. It can…

Cryptography and Security · Computer Science 2024-01-09 Oded Regev

We study the algorithmic task of testably learning general Massart halfspaces under the Gaussian distribution. In the testable learning setting, the aim is the design of a tester-learner pair satisfying the following properties: (1) if the…

Data Structures and Algorithms · Computer Science 2026-02-27 Ilias Diakonikolas , Giannis Iakovidis , Daniel M. Kane , Sihan Liu

We give a polynomial-time algorithm for learning high-dimensional halfspaces with margins in $d$-dimensional space to within desired TV distance when the ambient distribution is an unknown affine transformation of the $d$-fold product of an…

Machine Learning · Computer Science 2023-11-03 Xinyuan Cao , Santosh S. Vempala

We say that a classifier is \emph{adversarially robust} to perturbations of norm $r$ if, with high probability over a point $x$ drawn from the input distribution, there is no point within distance $\le r$ from $x$ that is classified…

Data Structures and Algorithms · Computer Science 2025-05-21 Jane Lange , Arsen Vasilyan

We study the complexity of smoothed agnostic learning of halfspaces on $\{\pm 1\}^n$ under uniform marginals in the model of~\cite{KM25}, where each input coordinate is independently flipped with probability $\sigma \in (0, {1}/{2})$. We…

Machine Learning · Computer Science 2026-05-14 Tim Sinen

We study {\em online} active learning of homogeneous halfspaces in $\mathbb{R}^d$ with adversarial noise where the overall probability of a noisy label is constrained to be at most $\nu$. Our main contribution is a Perceptron-like online…

Machine Learning · Computer Science 2021-06-24 Jie Shen

Binary classification in the classic PAC model exhibits a curious phenomenon: Empirical Risk Minimization (ERM) learners are suboptimal in the realizable case yet optimal in the agnostic case. Roughly speaking, this owes itself to the fact…

Machine Learning · Computer Science 2025-12-22 Julian Asilis , Mikael Møller Høgsgaard , Grigoris Velegkas

We establish new hardness results for decision tree optimization problems, adding to a line of work that dates back to Hyafil and Rivest in 1976. We prove, under randomized ETH, superpolynomial lower bounds for two basic problems: given an…

Computational Complexity · Computer Science 2022-10-13 Caleb Koch , Carmen Strassle , Li-Yang Tan