概率方法在有预算约束的黑盒二进制优化中的应用：传感器布置的应用
Probabilistic Approach to Black-Box Binary Optimization with Budget Constraints: Application to Sensor Placement
AI总结：
本文提出了一种概率方法，用于在预算约束下解决最优实验设计问题，通过条件伯努利模型扩展来建模预算约束，减少计算成本并避免软约束调参。
摘要：
本文提出了一种完全概率方法，用于在预算约束下解决最优实验设计问题。将实验设计视为随机变量，并与参数条件分布相关联，该分布本质上建模了预算约束。原始优化问题被替换为对原目标函数期望值的优化，然后对分布参数进行优化。所得到的最优参数（策略）用于采样二进制空间的可行区域，以生成原始优化问题的最优解估计。本文扩展了条件伯努利模型家族，以建模由总非零条目数（即预算约束）条件的随机变量。该方法（a）适用于具有非随机黑盒目标函数和预算约束的二进制优化问题；（b）仅对可行区域建模和采样，从而比使用软约束大大减少了计算成本；（c）不使用软约束，因此不需要调节正则化参数（例如以促进稀疏性），这通常具有挑战性。所提出的方法通过基于对流-扩散前向模型的最优传感器布置实验进行了数值验证。
英文摘要：
This paper presents a fully probabilistic approach for solving optimal experimental design problems under budget constraints. The experimental design is viewed as a random variable and is associated with a parametric conditional distribution that inherently models the budget constraints. The original optimization problem is replaced with an optimization over the expected value of the original objective, which is then optimized over the distribution parameters. The resulting optimal parameter (policy) is used to sample the feasible region of binary space to produce estimates of the optimal solution(s) of the original optimization problem. In this work we extend the family of conditional Bernoulli models to model the random variable conditioned by the total number of nonzero entries, that is, the budget constraint. This approach (a) is generally applicable to binary optimization problems with nonstochastic black-box objective functions and budget constraints; (b) employs conditional probabilities to model and sample only the feasible region and thus considerably reduces the computational cost compared with employing soft constraints; and (c) does not employ soft constraints and thus does not require tuning of a regularization parameter, for example to promote sparsity, which is generally challenging. The proposed approach is verified numerically using an optimal sensor placement experiment based on an advection-diffusion forward model in a parameter identification setup.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
