Epistemic Errors of Imperfect Multitask Learners When Distributions Shift

2025-05-29

AI Summary

This paper addresses cognitive uncertainty modeling under the concurrent challenges of imperfect source training, task heterogeneity, and target distribution shift in multi-task learning. Methodologically, it introduces a rigorously defined cognitive error and its decomposable upper bound, uniquely disentangling generalization error into independent contributions from learning processes (e.g., model bias, estimation error) and environmental factors (e.g., task dissimilarity, distributional shift). It formally defines negative transfer and derives verifiable theoretical conditions for its occurrence. Leveraging a Bayesian transfer learning framework and ε-neighborhood modeling of distribution shift, the paper establishes a general cognitive error upper bound, along with two specialized bounds—Bayesian transfer and ε-neighborhood shift bounds. Synthetic experiments validate both the efficacy of the negative transfer criterion and the interpretability of the error decomposition.

Technology Category

• Machine Learning: Transfer, Domain Adaptation, Multi-Task Learning
• Cognitive Modeling & Cognitive Systems: Adaptive Behavior
• Reasoning under Uncertainty: Other Foundations of Reasoning under Uncertainty

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• User Modeling, Personalization and Recommendation: User modeling for targeted and personalized online advertising
• Economics, Online Markets and Human Computation: Social networks and social learning

Abstract

When data are noisy, a statistical learner's goal is to resolve epistemic uncertainty about the data it will encounter at test-time, i.e., to identify the distribution of test (target) data. Many real-world learning settings introduce sources of epistemic uncertainty that can not be resolved on the basis of training (source) data alone: The source data may arise from multiple tasks (multitask learning), the target data may differ systematically from the source data tasks (distribution shift), and/or the learner may not arrive at an accurate characterization of the source data (imperfect learning). We introduce a principled definition of epistemic error, and provide a generic, decompositional epistemic error bound. Our error bound is the first to (i) consider epistemic error specifically, (ii) accommodate all the sources of epistemic uncertainty above, and (iii) separately attribute the error to each of multiple aspects of the learning procedure and environment. As corollaries of the generic result, we provide (i) epistemic error bounds specialized to the settings of Bayesian transfer learning and distribution shift within $epsilon$-neighborhoods, and (ii) a set of corresponding generalization bounds. Finally, we provide a novel definition of negative transfer, and validate its insights in a synthetic experimental setting.

Problem

• Resolve epistemic uncertainty in noisy data distributions
• Address multitask learning with distribution shift
• Quantify epistemic error in imperfect learning environments

Innovation

• Introduces principled epistemic error definition
• Provides decompositional epistemic error bound
• Specializes bounds for Bayesian transfer learning