Decomposition and Adaptive Sampling for Data-Driven Inverse Linear Optimization
This work addresses data-driven inverse linear optimization for applications like customer preference learning and production planning, representing an incremental improvement with novel algorithmic extensions.
The paper tackles the problem of inferring unknown cost vectors in linear programs from noisy optimal solution data, introducing a new formulation that recovers a less restrictive set of cost estimates and developing exact and decomposition algorithms for offline and online settings, with computational experiments showing significant reductions in computation and sampling efforts.
This work addresses inverse linear optimization where the goal is to infer the unknown cost vector of a linear program. Specifically, we consider the data-driven setting in which the available data are noisy observations of optimal solutions that correspond to different instances of the linear program. We introduce a new formulation of the problem that, compared to other existing methods, allows the recovery of a less restrictive and generally more appropriate admissible set of cost estimates. It can be shown that this inverse optimization problem yields a finite number of solutions, and we develop an exact two-phase algorithm to determine all such solutions. Moreover, we propose an efficient decomposition algorithm to solve large instances of the problem. The algorithm extends naturally to an online learning environment where it can be used to provide quick updates of the cost estimate as new data becomes available over time. For the online setting, we further develop an effective adaptive sampling strategy that guides the selection of the next samples. The efficacy of the proposed methods is demonstrated in computational experiments involving two applications, customer preference learning and cost estimation for production planning. The results show significant reductions in computation and sampling efforts.