SMGO - $Δ$：在具有黑盒约束的全局Optimization中平衡谨慎和奖励
SMGO-$Δ$: Balancing Caution and Reward in Global Optimization with Black-Box Constraints
摘要：
在所有科学和工程领域的众多应用中，存在最优化问题，其中目标函数和约束都没有封闭形式的表达式，或者太复杂而无法分析管理，只能通过实验来评估。为了解决这些问题，我们设计了一个全局优化技术的黑箱目标和约束的问题。假设Lipschitz连续的成本和约束函数，集成员框架被采用来建立一个代理模型的优化程序，这是用于开发和勘探例程。由此产生的算法，命名为集成员全局优化与黑盒约束（SMGO- $Δ$），具有一个可调的风险参数，用户可以直观地调整权衡安全，剥削和探索。该算法的理论性质的推导，和优化性能进行了比较，从文献中的几个基准的代表性技术。最后，它是测试和比较约束贝叶斯优化的情况下，研究有关模型预测控制调整的伺服机构的干扰和植物的不确定性，解决实际激励的任务级约束。
英文摘要：
In numerous applications across all science and engineering areas, there are optimization problems where both the objective function and the constraints have no closed-form expression or are too complex to be managed analytically, that they can only be evaluated through experiments. To address such issues, we design a global optimization technique for problems with black-box objective and constraints. Assuming Lipschitz continuity of the cost and constraint functions, a Set Membership framework is adopted to build a surrogate model of the optimization program, that is used for exploitation and exploration routines. The resulting algorithm, named Set Membership Global Optimization With Black-Box Constraints (SMGO-$Δ$), features one tunable risk parameter, which the user can intuitively adjust to trade-off safety, exploitation, and exploration. The theoretical properties of the algorithm are derived, and the optimization performance is compared with representative techniques from the literature in several benchmarks. Lastly, it is tested and compared with constrained Bayesian optimization in a case study pertaining to model predictive control tuning for a servomechanism with disturbances and plant uncertainties, addressing practically-motivated task-level constraints.
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