We present a novel stochastic approach to binary optimization for optimal experimental design (OED) for Bayesian inverse problems governed by mathematical models such as partial differential equations. The OED utility function, namely, the regularized optimality criterion, is cast into a stochastic objective function in the form of an expectation over a multivariate Bernoulli distribution. The probabilistic objective is then solved by using a stochastic optimization routine to find an optimal observational policy. The proposed approach is analyzed from an optimization perspective and also from a machine learning perspective with correspondence to policy gradient reinforcement learning. The approach is demonstrated numerically by using an idealized two-dimensional Bayesian linear inverse problem, and validated by extensive numerical experiments carried out for sensor placement in a parameter identification setup.
翻译:我们提出了一种新颖的二进制优化方法,以优化贝耶斯人受部分差异方程式等数学模型制约的逆向问题的最佳实验设计(OED)。OED的实用功能,即正规化最佳性标准,以对多变量伯努利分布的预期形式,被抛入一个随机客观功能。然后,通过使用随机优化优化常规来找到最佳观测政策,来解决概率目标。从优化角度和机器学习的角度,从与政策梯度强化学习的对应角度,对拟议方法进行分析。这种方法通过使用理想化的二维贝耶斯线性反向问题,并通过在参数识别设置中为传感器定位而进行的大量数字实验加以验证,从数字角度加以证明。