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Decision-focused learning is a promising development for contextualoptimisation. It enables us to train prediction models that reflect thecontextual sensitivity structure of the problem. However, there have beenlimited attempts to extend this paradigm to robust optimisation. We propose adouble implicit layer model for training prediction models with respect torobust decision loss in uncertain convex quadratically constrained quadraticprograms (QCQP). The first layer solves a deterministic version of the problem,the second layer evaluates the worst case realisation for an uncertainty setcentred on the observation given the decisions obtained from the first layer.This enables us to learn model parameterisations that lead to robust decisionswhile only solving a simpler deterministic problem at test time. Additionally,instead of having to solve a robust counterpart we solve two smaller andpotentially easier problems in training. The second layer (worst case problem)can be seen as a regularisation approach for predict-and-optimise by fitting toa neighbourhood of problems instead of just a point observation. We motivaterelaxations of the worst-case problem in cases of uncertainty sets that wouldotherwise lead to trust region problems, and leverage various relaxations todeal with uncertain constraints. Both layers are typically strictly convex inthis problem setting and thus have meaningful gradients almost everywhere. Wedemonstrate an application of this model on simulated experiments. The methodis an effective regularisation tool for decision-focused learning for uncertainconvex QCQPs.

Learning Deterministic Surrogates for Robust Convex QCQPs