Decomposition and Adaptive Sampling for Data-Driven Inverse Linear Optimization

This work addresses inverse linear optimization, where the goal is to infer unknown cost vector of a program. Specifically, we consider data-driven setting in which available data are noisy observations optimal solutions that correspond different instances We introduce new formulation problem that, compared with other existing methods, allows recovery less restrictive and generally more appropriate admissible set estimates. It can be shown this optimization yields finite number solutions, develop an exact two-phase algorithm determine all such solutions. Moreover, propose efficient decomposition solve large problem. The extends naturally online learning environment it used provide quick updates estimate as become over time. For setting, further effective adaptive sampling strategy guides selection next samples. efficacy proposed methods demonstrated computational experiments involving two applications: customer preference estimation for production planning. results show significant reductions computation efforts. Summary Contribution: Using facilitate decision making at core operations research. (i.e., optimization), aims models from data. is, conceptually computationally, challenging Here, up scale has not been addressed previously. performance improved by substantially reduces required points.