Derivative-Free Decision-Focused Learning zur Plannung von Meersschutzgebieten

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Decision-focused learning (DFL) incorporates learned models into the solution process for optimization problems under uncertainty, thus using data to make better decisions. However, harnessing the power of learned models (decision trees, neural networks, etc.) within an optimization method is challenging, as the loss function for training a machine learning (ML) model is generally not compatible with the objective function of the optimization problem. This poses a significant obstacle, as learned models are not aligned with the goals of the optimization. Thus, given an optimization problem with uncertain parameters, the goal of DFL is to learn predictive models for the uncertain parameters that consider the cost (or profit) of the decisions. DFL typically seeks a differentiable formulation of the optimization problem so that backpropagation can be performed end-to-end. That is, information moves backwards through the optimization problem into the learned model. While this is a powerful paradigm for connecting learning and optimization, it has a key weakness: modeling problems with a derivative is extremely challenging and usually relies on surrogate models that only approximate the optimization problem. We propose a derivative-free DFL (DF-DFL) method by embedding learned models into a heuristic solution procedure and expose the parameters of these models to an algorithm that can tune parameters of the optimization approach and the learned models. This unifies the loss function of the learning and optimization without a derivative, allowing models to be found that lead directly to high-quality decisions. From a practical perspective, our approach has several compelling properties: First, it does not rely of surrogate loss functions which may form a poor approximation of the true problem. Second, our approach can deal with uncertain parameters in the constraints of the problem, whereas classical DFL approaches only handle objective functions affected by uncertainty. Third, our approach is attractive from a computational perspective since after training, it only needs to solve a deterministic optimization problem that does not scale in the size of the uncertain data. The DF-DFL method is motivated by a critical application for protecting biodiversity, namely the design of marine protected areas (MPAs). The DF-DFL approach is particularly attractive for solving this problem setting, as it can efficiently deal with uncertain parameters arising in any part of the problem. We will construct DFL-based models of optimizing MPAs, thus providing a powerful new method (DF-DFL), as well as giving decision makers a critical tool for making difficult conservation decisions under uncertainty.