面向决策的学习与可微分子模最大化用于车辆路径问题
Decision-Oriented Learning with Differentiable Submodular Maximization for Vehicle Routing Problem
AI总结：
针对移动充电站车辆路径问题，本文提出将子模最大化任务优化作为可微分层嵌入预测模型并端到端训练，从而获得比预测与优化分离方法更优的路径决策。
摘要：
我们研究学习一个将上下文观测（输入）映射到子模函数参数（输出）的函数这一问题。我们的启发性案例研究是一类特定的车辆路径问题，其中一组无人地面车辆（UGV）可以充当移动充电站，为执行持续监控任务的一组无人飞行器（UAV）充电。我们希望学习从对 UAV 任务路径和风场的观测到子模目标函数参数的映射，该目标函数描述 UAV 降落位置的分布。传统上，这样的学习问题被作为一个预测阶段独立求解，而没有考虑下游任务优化阶段。然而，预测中使用的损失函数可能与我们的最终目标（即良好的路径决策）不一致。在孤立的预测阶段表现良好并不一定能在下游路径任务中带来良好决策。本文提出一个框架，将任务优化作为预测阶段中的一个可微分层纳入其中。该框架允许对预测模型进行端到端训练，而无需使用仅针对预测性能的人工设计中间损失。在所提出的框架中，通过向确定性算法引入随机扰动（即随机平滑），使任务优化（子模最大化）变得可微分。我们使用合成数据证明了所提框架的有效性。移动充电站路径问题的实验结果表明，与预测—优化分离方法相比，所提框架能够产生更好的路径决策，例如平均充电 UAV 数量有所增加。
英文摘要：
We study the problem of learning a function that maps context observations (input) to parameters of a submodular function (output). Our motivating case study is a specific type of vehicle routing problem, in which a team of Unmanned Ground Vehicles (UGVs) can serve as mobile charging stations to recharge a team of Unmanned Ground Vehicles (UAVs) that execute persistent monitoring tasks. {We want to learn the mapping from observations of UAV task routes and wind field to the parameters of a submodular objective function, which describes the distribution of landing positions of the UAVs .} Traditionally, such a learning problem is solved independently as a prediction phase without considering the downstream task optimization phase. However, the loss function used in prediction may be misaligned with our final goal, i.e., a good routing decision. Good performance in the isolated prediction phase does not necessarily lead to good decisions in the downstream routing task. In this paper, we propose a framework that incorporates task optimization as a differentiable layer in the prediction phase. Our framework allows end-to-end training of the prediction model without using engineered intermediate loss that is targeted only at the prediction performance. In the proposed framework, task optimization (submodular maximization) is made differentiable by introducing stochastic perturbations into deterministic algorithms (i.e., stochastic smoothing). We demonstrate the efficacy of the proposed framework using synthetic data. Experimental results of the mobile charging station routing problem show that the proposed framework can result in better routing decisions, e.g. the average number of UAVs recharged increases, compared to the prediction-optimization separate approach.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
