What Data Enables Optimal Decisions? An Exact Characterization for Linear Optimization

Omar Bennouna, Amine Bennouna, Saurabh Amin, Asuman E. Ozdaglar

Keywords: data informativeness, linear optimization, Blackwell's informativeness theory, data value, data-driven decision-making

Abstract:

We study the fundamental question of how informative a dataset is for solving a given decision-making task. In our setting, the dataset provides partial information about unknown parameters that influence task outcomes. Focusing on linear programs, we characterize when a dataset is sufficient to recover an optimal decision, given an uncertainty set on the cost vector. Our main contribution is a sharp geometric characterization that identifies the directions of the cost vector that matter for optimality, relative to the task constraints and uncertainty set.
We further develop a practical algorithm that, for a given task, constructs a minimal or least-costly sufficient dataset.
Our results reveal that small, well-chosen datasets can often fully determine optimal decisions---offering a principled foundation for task-aware data selection.

Primary Area: Theory (e.g., control theory, learning theory, algorithmic game theory)

Submission Number: 26432