Derivative-Free Decision-Focused Learning zur Plannung von Meersschutzgebieten

决策聚焦学习（DFL）将学习到的模型纳入不确定性下优化问题的解决过程，从而使用数据做出更好的决策。然而，利用学习模型（决策树，神经网络等）的力量。在优化方法中，这是具有挑战性的，因为用于训练机器学习（ML）模型的损失函数通常与优化问题的目标函数不兼容。这构成了一个重大障碍，因为学习的模型与优化的目标不一致。因此，给定一个具有不确定参数的优化问题，DFL的目标是学习考虑决策成本（或利润）的不确定参数的预测模型。DFL通常寻求优化问题的可微分公式，以便可以端到端地执行反向传播。也就是说，信息通过优化问题向后移动到学习模型中。虽然这是连接学习和优化的强大范例，但它有一个关键的弱点：用导数建模问题极具挑战性，并且通常依赖于仅近似优化问题的代理模型。我们提出了一种无导数的DFL（DF-DFL）方法，通过将学习模型嵌入到启发式求解过程中，并将这些模型的参数暴露给一种算法，该算法可以调整优化方法和学习模型的参数。这统一了学习和优化的损失函数，而无需导数，从而可以找到直接导致高质量决策的模型。从实际的角度来看，我们的方法有几个引人注目的属性：首先，它不依赖于代理损失函数，这可能会形成一个真正的问题的近似差。其次，我们的方法可以处理不确定的参数的约束问题，而经典的DFL方法只处理目标函数的不确定性。第三，从计算的角度来看，我们的方法是有吸引力的，因为在训练之后，它只需要解决一个确定性的优化问题，而不需要扩展不确定数据的大小。DF-DFL方法的动机是保护生物多样性的关键应用，即海洋保护区（MPA）的设计。 DF-DFL方法对于解决此问题设置特别有吸引力，因为它可以有效地处理问题的任何部分中出现的不确定参数。我们将构建基于DFL的优化MPA的模型，从而提供一种功能强大的新方法（DF-DFL），并为决策者提供一种在不确定性下做出困难的保护决策的关键工具。

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.