Data-Driven Optimal Control
An Inverse Optimization Model and Algorithm
Y. Long (TU Delft - Mechanical Engineering)
P. Mohajerin Esfahani – Mentor (TU Delft - Mechanical Engineering)
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Abstract
In Inverse Optimization (IO), it is hypothesized that experts, when making decisions, implicitly engage in solving an optimization problem. If we can reconstruct this optimization problem using the decision data of the expert, then the behavior of the expert can be emulated. In this thesis, a novel inverse optimization model, Kernel Inverse Optimization Machine (KIOM), is proposed, utilizing kernel methods. Because its parameter space can be potentially infinite-dimensional, the model exhibits strong representation and generalization capabilities. Furthermore, empirical evidence is presented demonstrating the model’s ability to learn complex MuJoCo continuous control tasks. Subsequently, an algorithm for training KIOM, Sequential Selection Optimization (SSO), is proposed to address memory issues. SSO is a coordinate descent-based algorithm, and its memory requirements are nearly equal to the memory needed for solving one of its subproblems. Experimental results demonstrate that SSO converges to the optimal solution within a small number of iterations, highlighting its
efficiency.