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We study a sequential prediction problem in which an adversary is allowed to inject arbitrarily many adversarial instances in a stream of i.i.d. instances, but at each round, the learner may also abstain from making a prediction without…

Machine Learning · Computer Science 2026-03-19 Jialin Yu , Moïse Blanchard

We study online learning in the adversarial injection model introduced by [Goel et al. 2017], where a stream of labeled examples is predominantly drawn i.i.d.\ from an unknown distribution $\mathcal{D}$, but may be interspersed with…

Machine Learning · Computer Science 2026-02-24 Ezra Edelman , Surbhi Goel

We investigate the challenge of establishing stochastic-like guarantees when sequentially learning from a stream of i.i.d. data that includes an unknown quantity of clean-label adversarial samples. We permit the learner to abstain from…

Machine Learning · Computer Science 2025-04-22 Carolin Heinzler

We explore adversarial robustness in the setting in which it is acceptable for a classifier to abstain---that is, output no class---on adversarial examples. Adversarial examples are small perturbations of normal inputs to a classifier that…

Machine Learning · Computer Science 2019-11-27 Cassidy Laidlaw , Soheil Feizi

There has been much recent interest in understanding the continuum from adversarial to stochastic settings in online learning, with various frameworks including smoothed settings proposed to bridge this gap. We consider the more general and…

Machine Learning · Statistics 2025-06-19 Moïse Blanchard , Samory Kpotufe

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…

Machine Learning · Statistics 2011-04-28 Alexander Rakhlin , Karthik Sridharan , Ambuj Tewari

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 study the problem of learning predictors that are robust to adversarial examples with respect to an unknown perturbation set, relying instead on interaction with an adversarial attacker or access to attack oracles, examining different…

Machine Learning · Computer Science 2021-02-04 Omar Montasser , Steve Hanneke , Nathan Srebro

In the random-order model for online learning, the sequence of losses is chosen upfront by an adversary and presented to the learner after a random permutation. Any random-order input is \emph{asymptotically} equivalent to a stochastic…

Machine Learning · Computer Science 2025-10-06 Martino Bernasconi , Andrea Celli , Riccardo Colini-Baldeschi , Federico Fusco , Stefano Leonardi , Matteo Russo

Modern classification algorithms are susceptible to adversarial examples--perturbations to inputs that cause the algorithm to produce undesirable behavior. In this work, we seek to understand and extend adversarial examples across domains…

Machine Learning · Computer Science 2021-12-14 Volodymyr Kuleshov , Evgenii Nikishin , Shantanu Thakoor , Tingfung Lau , Stefano Ermon

In this paper, we investigate the following question: Can we obtain adversarially-trained models without training on adversarial examples? Our intuition is that training a model with inherent stochasticity, i.e., optimizing the parameters…

Machine Learning · Computer Science 2023-12-15 Ayoub Arous , Andres F Lopez-Lopera , Nael Abu-Ghazaleh , Ihsen Alouani

The susceptibility of modern machine learning classifiers to adversarial examples has motivated theoretical results suggesting that these might be unavoidable. However, these results can be too general to be applicable to natural data…

Machine Learning · Computer Science 2024-05-28 Ambar Pal , Jeremias Sulam , René Vidal

It is necessary to improve the performance of some special classes or to particularly protect them from attacks in adversarial learning. This paper proposes a framework combining cost-sensitive classification and adversarial learning…

Machine Learning · Computer Science 2022-06-24 Haojing Shen , Sihong Chen , Ran Wang , Xizhao Wang

We study high-dimensional distribution learning in an agnostic setting where an adversary is allowed to arbitrarily corrupt an $\varepsilon$-fraction of the samples. Such questions have a rich history spanning statistics, machine learning…

Data Structures and Algorithms · Computer Science 2019-03-18 Ilias Diakonikolas , Gautam Kamath , Daniel Kane , Jerry Li , Ankur Moitra , Alistair Stewart

The existence of evasion attacks during the test phase of machine learning algorithms represents a significant challenge to both their deployment and understanding. These attacks can be carried out by adding imperceptible perturbations to…

Machine Learning · Statistics 2018-06-07 Daniel Cullina , Arjun Nitin Bhagoji , Prateek Mittal

We provide algorithms for regression with adversarial responses under large classes of non-i.i.d. instance sequences, on general separable metric spaces, with provably minimal assumptions. We also give characterizations of learnability in…

Machine Learning · Computer Science 2023-06-13 Moïse Blanchard , Patrick Jaillet

In this work we present a formal theoretical framework for assessing and analyzing two classes of malevolent action towards generic Artificial Intelligence (AI) systems. Our results apply to general multi-class classifiers that map from an…

Machine Learning · Computer Science 2021-01-01 Ivan Y. Tyukin , Desmond J. Higham , Alexander N. Gorban

Prediction with the possibility of abstention (or selective prediction) is an important problem for error-critical machine learning applications. While well-studied in the classification setup, selective approaches to regression are much…

Machine Learning · Statistics 2023-09-29 Fedor Noskov , Alexander Fishkov , Maxim Panov

A common challenge across all areas of machine learning is that training data is not distributed like test data, due to natural shifts, "blind spots," or adversarial examples; such test examples are referred to as out-of-distribution (OOD)…

Machine Learning · Computer Science 2021-10-29 Adam Tauman Kalai , Varun Kanade

We present a transductive learning algorithm that takes as input training examples from a distribution $P$ and arbitrary (unlabeled) test examples, possibly chosen by an adversary. This is unlike prior work that assumes that test examples…

Machine Learning · Computer Science 2020-10-01 Shafi Goldwasser , Adam Tauman Kalai , Yael Tauman Kalai , Omar Montasser
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