Decision-Focused Sequential Experimental Design: A Directional Uncertainty-Guided Approach

Classical experimental design has traditionally focused on constructing design variables that facilitate the selection of models with high predictive accuracy. In decision-focused learning, however, the model that achieves the lowest prediction error may not coincide with the one that induces the best downstream decision. Motivated by this misalignment, we investigate appropriate criteria for sequential experimental design in decision-focused settings. Specifically, we consider a sequential data acquisition problem in which a learner adaptively selects samples to label, or equivalently, treatment responses to observe. Existing experimental design methods are inherently decision-blind: they aim to reduce predictive uncertainty, even though reductions in predictive error need not translate into improvements in decision quality. To bridge this gap, we introduce a directional uncertainty criterion that aligns predictive uncertainty with the structure of the downstream decision-making problem, in contrast to naïve decision-blind uncertainty quantification methods. We show that this transformation admits strong theoretical guarantees and achieves reduced sample complexity relative to decision-blind design.