We present a novel probabilistic approach for optimal path experimental design. In this approach a discrete path optimization problem is defined on a static navigation mesh, and trajectories are modeled as random variables governed by a parametric Markov policy. The discrete path optimization problem is then replaced with an equivalent stochastic optimization problem over the policy parameters, resulting in an optimal probability model that samples estimates of the optimal discrete path. This approach enables exploration of the utility function's distribution tail and treats the utility function of the design as a black box, making it applicable to linear and nonlinear inverse problems and beyond experimental design. Numerical verification and analysis are carried out by using a parameter identification problem widely used in model-based optimal experimental design.

翻译：本文提出了一种新颖的基于概率的最优路径实验设计方法。该方法在静态导航网格上定义离散路径优化问题，并将轨迹建模为由参数化马尔可夫策略控制的随机变量。随后，将离散路径优化问题转化为策略参数空间上的等效随机优化问题，从而得到能够采样最优离散路径估计的最优概率模型。该方法能够探索效用函数的分布尾部，并将实验设计的效用函数视为黑箱，使其可适用于线性和非线性反问题以及其他非实验设计场景。通过采用基于模型的最优实验设计中广泛使用的参数辨识问题，我们进行了数值验证与分析。