QuIP：通过整数规划处理具有多定性因素的昂贵模拟器的实验设计
QuIP: Experimental design for expensive simulators with many Qualitative factors via Integer Programming
AI总结：
本文提出名为QuIP的新框架，通过整数规划在Gaussian process代理模型下为具有多定性因素的昂贵模拟器设计实验，将初始和顺序设计转化为assignment problem实现高效全局优化，并在路径规划和火星车轨迹优化中验证了其有效性。
摘要：
在广泛的科学与工程问题中，常常需要探索和/或优化具有许多定性因素的昂贵模拟器。我们的动机应用在于路径规划——即探索用于导航的可行路径，这在机器人技术、手术规划和装配规划中发挥着重要作用。在这里，路径的可行性通过昂贵的虚拟实验来评估，且其参数空间通常是离散且高维的。因此，精心选择的实验设计对于及时决策至关重要。我们在此提出了一个名为QuIP的新框架，用于在具有可交换协方差函数的Gaussian process代理模型下，通过Integer Programming进行定性因素的实验设计。对于初始设计，我们证明了其渐近D-optimal design可以表述为运筹学中著名的assignment problem的一个变体，可以使用最先进的integer programming求解器高效地求解至全局最优。对于顺序设计（具体而言，用于active learning或black-box optimization），我们证明了其设计准则同样可以表述为assignment problem，从而能够利用现有求解器进行高效且可靠的优化。随后，我们在一组路径规划实验和火星车轨迹优化应用中，展示了QuIP相对于现有方法的有效性。
英文摘要：
The need to explore and/or optimize expensive simulators with many qualitative factors arises in broad scientific and engineering problems. Our motivating application lies in path planning - the exploration of feasible paths for navigation, which plays an important role in robotics, surgical planning and assembly planning. Here, the feasibility of a path is evaluated via expensive virtual experiments, and its parameter space is typically discrete and high-dimensional. A carefully selected experimental design is thus essential for timely decision-making. We propose here a novel framework, called QuIP, for experimental design of Qualitative factors via Integer Programming under a Gaussian process surrogate model with an exchangeable covariance function. For initial design, we show that its asymptotic D-optimal design can be formulated as a variant of the well-known assignment problem in operations research, which can be efficiently solved to global optimality using state-of-the-art integer programming solvers. For sequential design (specifically, for active learning or black-box optimization), we show that its design criterion can similarly be formulated as an assignment problem, thus enabling efficient and reliable optimization with existing solvers. We then demonstrate the effectiveness of QuIP over existing methods in a suite of path planning experiments and an application to rover trajectory optimization.
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