Data-driven Inverse Optimization (IO) is a form of Supervised Learning where it is assumed that the output data is found by means of an optimization problem that depends on the input data. IO uses this data to approximate the optimization problem as best as possible. In the case where one wants to emulate an expert operating in a dynamic environment, the dataset obtained by measuring the expert is often contained in a small, optimal part of the total state space of the environment. When a model trained on this data finds itself in a different part of the state space, it can behave erratically.
In this thesis, we will combine Inverse Optimization with the active learning method of Dataset Aggregation (DAgger) to test if this improves model performance in dynamic settings. DAgger is an iterative process where the system is steered by the learner, creating new input data for the expert to find the best actions. This new data is then used to train a new model.
Furthermore, we propose a new algorithm, fast-DAgger, that should converge faster than the DAgger algorithm, at the possible cost of performance in the final model.
IO models trained with the DAgger and fast-DAgger algorithms are tested and compared to IO models trained on static datasets. This is done for two case studies: the Dynamic Vehicle Routing Problem as proposed by the EURO meets Neurips 2022 Vehicle Routing Competition, and the game of Tetris.
Results show the potential of combining IO with DAgger. However, DAgger is not always better than training with a static dataset. DAgger can only be helpful when the static training data is limited to a part of the total state space and when this data does not generalize well to the total state space. The fast-DAgger algorithm did not show a significant speed-up compared to the normal DAgger algorithm in the case studies. However, this is very dependent on the specifics of the model and the hyperparameters of the DAgger algorithm.

In this work, Clebsch-Gordan coefficients are studied from both a quantum mechanical and a mathematical perspective. In quantum mechanics, Clebsch-Gordan coefficients arise when two quantum systems with a certain angular momentum are combined and the total angular momentum is to be found. We start by discussing the relevant postulates of quantum mechanics. From there we move on to a discussion of quantum angular momentum, the combining of quantum systems, and Clebsch-Gordan coefficients. Finally, an algorithm for calculating the Clebsch-Gordan coefficients is developed. A firm grasp of linear algebra is required to understand this quantum mechanical perspective. The mathematical perspective is rooted in representation theory. The Clebsch-Gordan coefficients show the decomposition of the tensor product of irreducible representations of the three dimensional rotation group into the direct sum of irreducible representations. We explain the necessary theory to understand how this works. This includes a discussion of irreducible unitary representations, spherical harmonics, direct sum representations, and tensor product representations. Some experience with group theory is required to understand the mathematical perspective.