Optimization powers most of machine learning, deep learning not the least. But what happens if you turn this around, and instead use machine learning to power optimization? This question challenges long-held beliefs in optimization and is at the forefront of so-called data-driven optimization—an emerging research field that aims to develop the next generation of optimization methods by combining different aspects of modern machine learning. As the following three examples show, the context determines which aspect is the most appropriate: (1) for stochastic optimization, a natural fit is probabilistic numerics, wherein conventional methods are reframed as probabilistic ones, (2) for constrained optimization graph neural networks, which model relations between variables as a graph, are well-suited, (3) if the goal is to embed the optimization solver in a larger system that you want to train end-to-end, then a good choice is differentiable programming, where the optimizer itself is made automatically differentiable. Since the field is still in its infancy, there are many exciting research problems to choose from, and the PhD student will have a large freedom in steering towards the ones he or she finds the most interesting.

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