Distribution-Free Sequential Prediction with Abstentions

2026-02-20

AI Summary

This study addresses distribution-free online sequence prediction with abstention, where the learner may choose to abstain from prediction to avoid misclassification in the presence of an arbitrary number of adversarial examples. The authors propose AbstainBoost, a boosting-based algorithm that leverages weak learners to achieve sublinear mistake bounds for any VC class without prior knowledge of the data distribution. This work establishes the first learnability guarantee with abstention for general VC classes under unknown distributions, revealing a polynomial trade-off between misclassification and erroneous abstentions, and provides matching theoretical lower bounds. The algorithm is robust to both oblivious and adaptive adversaries and offers strong theoretical guarantees even for structured hypothesis classes such as linear classifiers.

Technology Category

• Machine Learning: Online Learning & Bandits
• Game Theory and Economic Paradigms: Adversarial Learning
• Multiagent Systems: Adversarial Agents

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Economics, Online Markets and Human Computation: Data quality aspects of human-annotated datasets

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.

Problem

• distribution-free
• sequential prediction
• adversarial corruption
• abstention
• VC classes

Innovation

• distribution-free learning
• sequential prediction with abstentions
• adversarial robustness
• boosting
• VC classes