(415d) A Data-Driven Inverse Optimization Approach to Learning Surrogate Optimizers

Mathematical optimization has become indispensable for informing decisions in complex industrial systems. However, rigorous models of such systems tend to be nonlinear and nonconvex, which makes them computationally inefficient. In many cases such as real-time optimization of chemical plants, a safe and optimal operation hinges on solving these ‘hard’ optimization problems at frequent intervals. A common strategy is to replace the original model with a surrogate model of reduced computational complexity [1]. In this work, we introduce a data-driven inverse optimization [2] (IO) approach for constructing surrogate optimizers [3], which are surrogate models that are trained to obtain (almost) the same optimal solutions as the original optimization models. In contrast to traditional machine learning methods, IO allows the incorporation of domain knowledge in the form of explicit constraints and tends to be more data-efficient. Moreover, it allows the resulting models to be inherently interpretable.

Our work assumes that a parameterized convex optimization model can be trained to obtain optimal solutions that are similar to what the original model generates. Here, the IO problem is to determine the model parameters that minimize the difference between the true optimal solutions and the solutions obtained from solving the resulting learned optimization model. We formulate the bilevel program and apply a penalty block coordinate descent method [4] to solve the single-level KKT-based reformulation of the IO problem. We demonstrate the effectiveness of our method using several case studies including a nonlinear model predictive control example.

References:

1. Caballero, J. A. & Grossmann, I. E. An algorithm for the use of surrogate models in modular flowsheet optimization. AIChE J. 54, (2008).

2. Mohajerin Esfahani, P., Shafieezadeh-Abadeh, S., Hanasusanto, G. A. & Kuhn, D. Data-driven inverse optimization with imperfect information. Math. Program. 167, 191–234 (2018).

3. Krishnamoorthy, D., dos Santos, A., & Skogestad, S. Online Process Optimization Using a Surrogate Optimizer. 2019 AIChE Annual Meeting. AIChE.

4. Kleinert, T. & Schmidt, M. Computing Feasible Points of Bilevel Problems with a Penalty Alternating Direction Method. INFORMS J. Comput. (2020).