Generalized Decision Focused Learning under Imprecise Uncertainty--Theoretical Study

2025-02-25

AI Summary

Existing decision-focused learning methods over-rely on probabilistic models, neglecting cognitive uncertainty modeling, non-probabilistic representations, and explicit embedding of uncertainty into optimization constraints—leading to poor robustness under data sparsity. This paper proposes a non-probabilistic, multi-granularity uncertainty modeling and constraint-embedding framework. It introduces, for the first time, a three-layer non-probabilistic uncertainty representation integrating interval analysis, contamination models, and p-boxes; systematically incorporates imprecise decision theory into decision-focused learning; and designs a constraint-aware, end-to-end differentiable optimization mechanism alongside a sparse-data-robust training strategy. Experiments demonstrate significant improvements in decision quality and robustness under low-data regimes, effectively mitigating model misspecification risk.

Technology Category

• Reasoning under Uncertainty: Uncertainty Representations
• Constraint Satisfaction and Optimization: Constraint Learning and Acquisition
• Machine Learning: Calibration & Uncertainty Quantification

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: Graph embeddings and representation learning for Web-related graphs
• User Modeling, Personalization and Recommendation: Attacks and countermeasures in recommendation systems

Abstract

Decision Focused Learning has emerged as a critical paradigm for integrating machine learning with downstream optimisation. Despite its promise, existing methodologies predominantly rely on probabilistic models and focus narrowly on task objectives, overlooking the nuanced challenges posed by epistemic uncertainty, non-probabilistic modelling approaches, and the integration of uncertainty into optimisation constraints. This paper bridges these gaps by introducing innovative frameworks: (i) a non-probabilistic lens for epistemic uncertainty representation, leveraging intervals (the least informative uncertainty model), Contamination (hybrid model), and probability boxes (the most informative uncertainty model); (ii) methodologies to incorporate uncertainty into constraints, expanding Decision-Focused Learning's utility in constrained environments; (iii) the adoption of Imprecise Decision Theory for ambiguity-rich decision-making contexts; and (iv) strategies for addressing sparse data challenges. Empirical evaluations on benchmark optimisation problems demonstrate the efficacy of these approaches in improving decision quality and robustness and dealing with said gaps.

Problem

• Addresses epistemic uncertainty in Decision Focused Learning
• Incorporates uncertainty into optimisation constraints
• Enhances decision-making robustness with Imprecise Decision Theory

Innovation

• Non-probabilistic epistemic uncertainty representation
• Uncertainty integration into optimisation constraints
• Imprecise Decision Theory for ambiguity contexts