Generalized Decision Focused Learning under Imprecise Uncertainty--Theoretical Study
This work addresses the problem of integrating uncertainty into optimization for machine learning practitioners, offering incremental advancements in handling imprecise data and constraints.
The paper tackled the limitations of Decision Focused Learning by addressing epistemic uncertainty, non-probabilistic models, and uncertainty in constraints, introducing frameworks that improved decision quality and robustness in benchmark optimization problems.
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.