Informative Path Planning with Gaussian Processes: Error Bounds, Algorithms, and Benchmarks

Accurate environmental monitoring relies on Informative Path Planning (IPP) to deploy autonomous systems that maximize information gain. While Gaussian Processes (GPs) provide a robust mathematical foundation for modeling the environment, contemporary IPP approaches remain hindered by heuristic operational constraints and the lack of simultaneous theoretical guarantees for worst-case estimation error and approximation quality. Rather than introducing yet another heuristic, this paper presents a rigorous theoretical analysis of existing error bounds and algorithms to further develop the mathematical foundation for IPP.

By evaluating probabilistic and deterministic bounds on reconstruction error, we establish that predictive variance is the theoretically ideal optimization objective for GP-based IPP. Furthermore, we analyze GreedyCover, a recent approach for optimizing predictive variance, and demonstrate that its near-optimal approximation guarantee matches the fundamental hardness-of-approximation limit for the problem. Comprehensive benchmarking confirms that this approach delivers superior estimation accuracy and computational efficiency compared to prominent information-theoretic objectives and optimization methods used in IPP. Finally, this theoretical analysis establishes a rigorous, near-optimal foundation for discrete offline IPP under bounded uncertainty constraints, offering clear and principled guidance for future work in continuous-space and online formulations.