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The information complexity of a function $f$ is the minimum amount of information Alice and Bob need to exchange to compute the function $f$. In this paper we provide an algorithm for approximating the information complexity of an arbitrary…

Information Theory · Computer Science 2015-02-11 Mark Braverman , Jon Schneider

The information in an individual finite object (like a binary string) is commonly measured by its Kolmogorov complexity. One can divide that information into two parts: the information accounting for the useful regularity present in the…

Computational Complexity · Computer Science 2007-05-23 Paul Vitanyi

We revisit the problem of private online learning, in which a learner receives a sequence of $T$ data points and has to respond at each time-step a hypothesis. It is required that the entire stream of output hypotheses should satisfy…

Machine Learning · Computer Science 2025-11-11 Bo Li , Wei Wang , Peng Ye

We study the problem of online binary classification in settings where strategic agents can modify their observable features to receive a positive classification. We model the set of feasible manipulations by a directed graph over the…

Machine Learning · Computer Science 2024-07-17 Saba Ahmadi , Kunhe Yang , Hanrui Zhang

Classical complexity theory measures the cost of computing a function, but many computational tasks require committing to one valid output among several. We introduce determination depth -- the minimum number of sequential layers of…

Computational Complexity · Computer Science 2026-04-08 Joseph M. Hellerstein

In this paper we prove that the sample complexity of properly learning a class of Littlestone dimension $d$ with approximate differential privacy is $\tilde O(d^6)$, ignoring privacy and accuracy parameters. This result answers a question…

Machine Learning · Computer Science 2020-12-08 Badih Ghazi , Noah Golowich , Ravi Kumar , Pasin Manurangsi

We consider online and PAC learning of Littlestone classes subject to the constraint of approximate differential privacy. Our main result is a private learner to online-learn a Littlestone class with a mistake bound of…

Machine Learning · Statistics 2025-10-02 Xin Lyu

This paper is about the surprising interaction of a foundational result from model theory, about stability of theories, with algorithmic stability in learning. First, in response to gaps in existing learning models, we introduce a new…

Logic · Mathematics 2025-07-04 Maryanthe Malliaris , Shay Moran

We use algorithmic methods from online learning to explore some important objects at the intersection of model theory and combinatorics, and find natural ways that algorithmic methods can detect and explain (and improve our understanding…

Discrete Mathematics · Computer Science 2025-07-08 Maryanthe Malliaris , Shay Moran

We propose a new model for augmenting algorithms with predictions by requiring that they are formally learnable and instance robust. Learnability ensures that predictions can be efficiently constructed from a reasonable amount of past data.…

Machine Learning · Computer Science 2021-07-05 Thomas Lavastida , Benjamin Moseley , R. Ravi , Chenyang Xu

A general notion of information-related complexity applicable to both natural and man-made systems is proposed. The overall approach is to explicitly consider a rational agent performing a certain task with a quantifiable degree of success.…

Data Analysis, Statistics and Probability · Physics 2013-01-18 Eugene Perevalov , David Grace

We study the problem of learning robust classifiers where the classifier will receive a perturbed input. Unlike robust PAC learning studied in prior work, here the clean data and its label are also adversarially chosen. We formulate this…

Machine Learning · Computer Science 2026-03-02 Sajad Ashkezari

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…

Computational Complexity · Computer Science 2023-10-18 Matthias C. Caro

Contextual online decision-making problems with constraints appear in a wide range of real-world applications, such as adaptive experimental design under safety constraints, personalized recommendation with resource limits, and dynamic…

Machine Learning · Statistics 2025-05-23 Haichen Hu , David Simchi-Levi , Navid Azizan

Iterative algorithms solve problems by taking steps until a solution is reached. Models in the form of Deep Thinking (DT) networks have been demonstrated to learn iterative algorithms in a way that can scale to different sized problems at…

Machine Learning · Computer Science 2024-11-01 Jay Bear , Adam Prügel-Bennett , Jonathon Hare

In this paper, we study arbitrary infinite binary information systems each of which consists of an infinite set called universe and an infinite set of two-valued functions (attributes) defined on the universe. We consider the notion of a…

Computational Complexity · Computer Science 2022-01-05 Mikhail Moshkov

This paper studies classification with an abstention option in the online setting. In this setting, examples arrive sequentially, the learner is given a hypothesis class $\mathcal H$, and the goal of the learner is to either predict a label…

Machine Learning · Computer Science 2016-09-29 Chicheng Zhang , Kamalika Chaudhuri

We consider the arithmetic complexity of index sets of uniformly computably enumerable families learnable under different learning criteria. We determine the exact complexity of these sets for the standard notions of finite learning,…

Logic · Mathematics 2013-03-01 Achilles Beros

The domain-independent universal Normalized Information Distance based on Kolmogorov complexity has been (in approximate form) successfully applied to a variety of difficult clustering problems. In this paper we investigate theoretical…

Information Theory · Computer Science 2025-07-30 Marcus Hutter

The nature of concept learning is a core question in cognitive science. Theories must account for the relative difficulty of acquiring different concepts by supervised learners. For a canonical set of six category types, two distinct…

Information Theory · Computer Science 2015-03-03 Andreas D. Pape , Kenneth J. Kurtz , Hiroki Sayama