论文标题
最佳实验设计问题的一阶方法具有约束约束
First-Order Methods for Optimal Experimental Design Problems with Bound Constraints
论文作者
论文摘要
我们考虑了概率度量单纯的一类凸优化问题。我们的框架包括最佳实验设计（OED）问题，其中设计空间的度量表明选择了哪些实验。由于存在其他约束约束，该度量具有Lebesgue密度，并且该问题可以作为在本质界限函数的空间上作为优化问题。对于这类问题，我们考虑了两种一阶方法，包括Fista和一种近端外推梯度方法，以及合适的停止标准。最后，讨论了针对每个迭代中子问题维度的加速策略。整个论文中的分析伴随着数值实验。
We consider a class of convex optimization problems over the simplex of probability measures. Our framework comprises optimal experimental design (OED) problems, in which the measure over the design space indicates which experiments are being selected. Due to the presence of additional bound constraints, the measure possesses a Lebesgue density and the problem can be cast as an optimization problem over the space of essentially bounded functions. For this class of problems, we consider two first-order methods including FISTA and a proximal extrapolated gradient method, along with suitable stopping criteria. Finally, acceleration strategies targeting the dimension of the subproblems in each iteration are discussed. Numerical experiments accompany the analysis throughout the paper.
