QuIP: Experimental design for expensive simulators with many Qualitative factors via Integer Programming

2025-01-24

AI Summary

Experimental design for high-dimensional, discrete, and computationally expensive simulators—such as robotic or rover path planning—with qualitative factors remains challenging due to the combinatorial complexity and lack of theoretical guarantees in existing approaches. Method: This paper proposes an efficient framework integrating integer programming with a switchable-covariance Gaussian process surrogate model tailored for qualitative inputs. It unifies D-optimal initial design and sequential active learning into a globally solvable assignment problem—a first-of-its-kind formulation. Contribution/Results: The framework ensures statistical optimality and global convergence, overcoming the efficiency and theoretical limitations of heuristic methods in qualitative factor spaces. Evaluated on multiple path-planning and planetary rover trajectory optimization tasks, it achieves 3–5× improvement in experimental design efficiency over state-of-the-art methods.

Technology Category

• Search and Optimization: Sampling/Simulation-based Search
• Intelligent Robots: Learning & Optimization for ROB
• Constraint Satisfaction and Optimization: Mixed Discrete/Continuous Optimization

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Economics, Online Markets and Human Computation: Data quality aspects of human-annotated datasets
• User Modeling, Personalization and Recommendation: User modeling and simulation for interactive and conversational systems

Abstract

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.

Problem

• Optimal Experimental Design
• Qualitative Elements
• Multi-parameter Path Planning

Innovation

• QuIP
• Optimization
• Experimental Design