Misspecified Universal Learning
2026-05-11 • Information Theory
Information Theory
AI summaryⓘ
The authors study a learning problem where the models a learner uses might not perfectly match how the real data is generated. They focus on how to minimize the worst-case difference in predictions (called regret) when the true data process might be outside the assumed models. Building on past work, they find the best possible universal method for learning under these uncertain conditions. Their approach works for different types of data and learning setups, whether data comes all at once or over time, and whether labels are available or not.
universal learningmodel misspecificationlog-lossminimax regrethypothesis classonline learningbatch learningsupervised learningunsupervised learningdata-generating process
Authors
Shlomi Vituri, Meir Feder
Abstract
This paper addresses the problem of universal learning under model misspecification with log-loss. In this setting, the learner operates with a hypothesis class of models denoted by $Θ$, while the true data-generating process belongs to a broader class $Φ\supset Θ$, and may lie outside the assumed hypothesis space. Classical approaches have characterized the minimax regret and identified optimal universal learners in both the well-specified stochastic and individual deterministic frameworks. The misspecified setting has received comparatively less attention, although several important results have emerged in recent years. Extending these foundations, we analyze the minimax regret in the misspecified setting and derive the corresponding optimal universal learner. We propose this formulation as a unified framework for universal learning, applicable to any form of uncertainty in the data-generating process, across both online and batch data arrival modes, as well as supervised and unsupervised learning tasks.