论文标题
选择最佳优化系统
Selecting the Best Optimizing System
论文作者
论文摘要
我们制定选择最佳优化系统（SBO）问题，并为这些问题提供解决方案。在SBO问题中，有限数量的系统是竞争者。在每个系统内部，连续的决策变量会影响系统的预期性能。 SBO问题根据其自己最佳选择的决定选择最佳决定的预期性能比较了不同的系统，而无需提前了解系统的预期性能或每个系统内部的优化决策。我们设计了易于实施的算法，这些算法可自适应地选择系统，并选择评估嘈杂系统性能的决定，依次消除劣质系统，并最终在花费用户指定的预算之后将系统作为最佳系统。所提出的算法集成了随机梯度下降方法和顺序消除方法，以同时利用每个系统内部的结构并进行跨系统进行比较。对于拟议的算法，随着预算增长到无限，我们证明了错误选择概率的收敛速率为零。我们进行了三个代表SBO问题的实际情况的数值示例。我们提出的算法在一系列问题设置和采样预算的范围内，在基准算法的错误选择的可能性方面表现出一致，更强的性能。
We formulate selecting the best optimizing system (SBOS) problems and provide solutions for those problems. In an SBOS problem, a finite number of systems are contenders. Inside each system, a continuous decision variable affects the system's expected performance. An SBOS problem compares different systems based on their expected performances under their own optimally chosen decision to select the best, without advance knowledge of expected performances of the systems nor the optimizing decision inside each system. We design easy-to-implement algorithms that adaptively chooses a system and a choice of decision to evaluate the noisy system performance, sequentially eliminates inferior systems, and eventually recommends a system as the best after spending a user-specified budget. The proposed algorithms integrate the stochastic gradient descent method and the sequential elimination method to simultaneously exploit the structure inside each system and make comparisons across systems. For the proposed algorithms, we prove exponential rates of convergence to zero for the probability of false selection, as the budget grows to infinity. We conduct three numerical examples that represent three practical cases of SBOS problems. Our proposed algorithms demonstrate consistent and stronger performances in terms of the probability of false selection over benchmark algorithms under a range of problem settings and sampling budgets.
