Decision-focused learning is a promising development for contextual optimisation. It enables us to train prediction models that reflect the contextual sensitivity structure of the problem. However, there have been limited attempts to extend this paradigm to robust optimisation. We propose a double implicit layer model for training prediction models with respect to robust decision loss in uncertain convex quadratically constrained quadratic programs (QCQP). The first layer solves a deterministic version of the problem, the second layer evaluates the worst case realisation for an uncertainty set centred on the observation given the decisions obtained from the first layer. This enables us to learn model parameterisations that lead to robust decisions while only solving a simpler deterministic problem at test time. Additionally, instead of having to solve a robust counterpart we solve two smaller and potentially easier problems in training. The second layer (worst case problem) can be seen as a regularisation approach for predict-and-optimise by fitting to a neighbourhood of problems instead of just a point observation. We motivate relaxations of the worst-case problem in cases of uncertainty sets that would otherwise lead to trust region problems, and leverage various relaxations to deal with uncertain constraints. Both layers are typically strictly convex in this problem setting and thus have meaningful gradients almost everywhere. We demonstrate an application of this model on simulated experiments. The method is an effective regularisation tool for decision-focused learning for uncertain convex QCQPs.

决策导向学习是上下文优化的一种有前景的发展，而我们提出了一个双重隐式层模型，用于训练预测模型以实现对不确定凸二次约束二次规划问题中健壮决策损失的训练。该模型是决策导向学习不确定凸QCQPs的有效正则化工具。

学习确定性代理关系以实现鲁棒的凸优化问题