Distribution-Free Sequential Prediction with Abstentions
arXiv:2602.17918v1 Announce Type: new Abstract: 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 \emph{abstain} from making a prediction without incurring any penalty if the instance was indeed corrupted. This semi-adversarial setting naturally sits between the classical stochastic case with i.i.d.\ instances for which function classes with finite VC dimension are learnable; and the adversarial case with arbitrary instances, known to be significantly more restrictive. For this problem, Goel et al. (2023) showed that, if the learner knows the distribution $\mu$ of clean samples in advance, learning can be achieved for all VC classes without restrictions on adversary corruptions. This is, however, a strong assumption in both theory and practice: a natural question is whether similar learning guarantees can be achieved without prior distribut
arXiv:2602.17918v1 Announce Type: new Abstract: 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 \emph{abstain} from making a prediction without incurring any penalty if the instance was indeed corrupted. This semi-adversarial setting naturally sits between the classical stochastic case with i.i.d.\ instances for which function classes with finite VC dimension are learnable; and the adversarial case with arbitrary instances, known to be significantly more restrictive. For this problem, Goel et al. (2023) showed that, if the learner knows the distribution $\mu$ of clean samples in advance, learning can be achieved for all VC classes without restrictions on adversary corruptions. This is, however, a strong assumption in both theory and practice: a natural question is whether similar learning guarantees can be achieved without prior distributional knowledge, as is standard in classical learning frameworks (e.g., PAC learning or asymptotic consistency) and other non-i.i.d.\ models (e.g., smoothed online learning). We therefore focus on the distribution-free setting where $\mu$ is \emph{unknown} and propose an algorithm \textsc{AbstainBoost} based on a boosting procedure of weak learners, which guarantees sublinear error for general VC classes in \emph{distribution-free} abstention learning for oblivious adversaries. These algorithms also enjoy similar guarantees for adaptive adversaries, for structured function classes including linear classifiers. These results are complemented with corresponding lower bounds, which reveal an interesting polynomial trade-off between misclassification error and number of erroneous abstentions.
Executive Summary
This article explores distribution-free sequential prediction with abstentions, where a learner can abstain from making a prediction without penalty if the instance is corrupted. The authors propose an algorithm, AbstainBoost, which guarantees sublinear error for general VC classes in the distribution-free abstention learning setting. The results are complemented with lower bounds, revealing a trade-off between misclassification error and erroneous abstentions. The study contributes to the understanding of semi-adversarial settings, bridging the gap between stochastic and adversarial cases.
Key Points
- ▸ The article studies a sequential prediction problem with abstentions in a semi-adversarial setting
- ▸ The authors propose the AbstainBoost algorithm, which guarantees sublinear error for general VC classes
- ▸ The results are applicable to both oblivious and adaptive adversaries, with extensions to structured function classes
Merits
Robustness to Adversarial Attacks
The AbstainBoost algorithm demonstrates robustness to adversarial attacks, ensuring sublinear error rates even in the presence of corrupted instances.
Demerits
Computational Complexity
The boosting procedure used in AbstainBoost may incur significant computational costs, potentially limiting its applicability in real-time prediction scenarios.
Expert Commentary
The article makes a significant contribution to the field of machine learning by providing a robust and efficient algorithm for distribution-free sequential prediction with abstentions. The AbstainBoost algorithm's ability to guarantee sublinear error rates in the presence of adversarial attacks demonstrates its potential for real-world applications. However, further research is needed to address the computational complexity of the algorithm and explore its applicability in various domains. The study's findings also highlight the importance of considering the interplay between robustness and accuracy in machine learning models, particularly in high-stakes applications.
Recommendations
- ✓ Future research should focus on optimizing the computational complexity of the AbstainBoost algorithm to enable its deployment in real-time prediction scenarios.
- ✓ The development of more efficient and robust algorithms for distribution-free sequential prediction with abstentions should be a priority, with potential applications in areas such as cybersecurity and healthcare.
