Generalized Decision Focused Learning under Imprecise Uncertainty--Theoretical Study

TL;DR

This paper advances Decision Focused Learning by incorporating non-probabilistic epistemic uncertainty models, integrating uncertainty into constraints, and applying Imprecise Decision Theory to enhance robustness and decision quality in uncertain environments.

Contribution

It introduces novel frameworks for representing epistemic uncertainty, incorporates uncertainty into optimization constraints, and applies Imprecise Decision Theory, addressing key gaps in existing methodologies.

Findings

Improved decision robustness under epistemic uncertainty.

Effective integration of uncertainty into optimization constraints.

Enhanced decision quality demonstrated on benchmark problems.

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.