论文标题
在稀疏高斯过程回归中最小化最差的最差案例错误的信息计划
Informative Planning for Worst-Case Error Minimisation in Sparse Gaussian Process Regression
论文作者
论文摘要
我们提出了一个计划框架，以最大程度地减少稀疏高斯过程（GP）回归中确定性的最坏情况误差。我们首先使用插值理论在繁殖内核希尔伯特空间（RKHSS）上使用界噪声来得出与稀疏GP回归结合的通用最差误差。通过利用稀疏GP回归中心的条件独立性（CI）假设，我们表明可以通过解决后熵最小化问题来实现最差的案例误差最小化。反过来，使用高斯信念空间规划算法解决了后熵最小化问题。我们证实了在简单的一维示例中绑定的提出的最坏情况误差，并在复杂流场中的2D车辆模拟中测试计划框架。我们的结果表明，所提出的后熵最小化方法可有效地最大程度地减少确定性误差，并且在固定诱导点时胜过常规的测量熵最大化公式。
We present a planning framework for minimising the deterministic worst-case error in sparse Gaussian process (GP) regression. We first derive a universal worst-case error bound for sparse GP regression with bounded noise using interpolation theory on reproducing kernel Hilbert spaces (RKHSs). By exploiting the conditional independence (CI) assumption central to sparse GP regression, we show that the worst-case error minimisation can be achieved by solving a posterior entropy minimisation problem. In turn, the posterior entropy minimisation problem is solved using a Gaussian belief space planning algorithm. We corroborate the proposed worst-case error bound in a simple 1D example, and test the planning framework in simulation for a 2D vehicle in a complex flow field. Our results demonstrate that the proposed posterior entropy minimisation approach is effective in minimising deterministic error, and outperforms the conventional measurement entropy maximisation formulation when the inducing points are fixed.
