Integrated Learning and Optimization

Statistical learning and mathematical optimization are both essential components of modern computational decision-support systems. Traditionally, learning and optimization have been applied sequentially, where data-driven approaches are used to construct models and predict parameters, which are then input into an optimization model to derive optimal decisions. In our work, we are interested in exploring approaches that apply learning and optimization jointly to gain further synergies.

In operational problems, e.g. model predictive control and production scheduling, the same optimization problem is solved frequently with different input parameters as time proceeds and new information arrives. However, the computational complexity of the optimization problem often presents a challenge where the long solution time renders it unsuitable for real-time applications. A common approach to tackling this challenge is to perform the online optimization with a surrogate model, which is an approximation of the original model that can be solved more efficiently. Typically, one tries to replace complicating equations that are embedded in the optimization problem with simpler ones. Here, a major underlying assumption is that a surrogate model that provides a good approximation of the original set of equations will, once incorporated into the optimization problem, also lead to solutions that are close to the true optimal solutions. However, it is unclear whether or under what conditions this assumption holds.

In decision-focused surrogate modeling (DFSM), we train the surrogate model with the ultimate goal of making decisions using the resulting optimization model in mind. As illustrated in the schematic below, it involves solving the original optimization problem offline with different model inputs to obtain the corresponding optimal decisions, resulting in a dataset where each data point is an input-decision pair. We then learn from the given data a surrogate optimization model that has a simpler form and directly minimizes the decision prediction error. We develop DFSM approaches for different classes of optimization problems and also integrate them into other algorithmic frameworks such as decomposition methods.

• Dixit, S., Gupta, R., & Zhang, Q. (2025). Decision-focused surrogate modeling for mixed-integer linear optimization. Transactions on Machine Learning Research.
• Gupta, R. & Zhang, Q. (2024). Data-driven decision-focused surrogate modeling. AIChE Journal, 70(4), e18338.