选择最优优化系统
Selecting the Best Optimizing System
AI总结：
本文提出选择最优优化系统（SBOS）问题，设计了结合随机梯度下降与顺序淘汰的自适应算法，并证明其错误选择概率随预算增长以指数速率收敛至零，实验验证了其优于基准算法的性能。
摘要：
我们提出了选择最优优化系统（SBOS）问题并为其提供了解决方案。在SBOS问题中，有限数量的系统作为竞争者。在每个系统内部，一个连续决策变量影响系统的期望性能。SBOS问题基于各系统在自身最优选择决策下的期望性能来比较不同系统以选出最优系统，而无需事先了解各系统的期望性能或系统内部的优化决策。我们设计了易于实现的算法，该算法自适应地选择系统并选择决策以评估含噪声的系统性能，顺序淘汰劣质系统，并在花费用户指定预算后最终推荐最优系统。所提算法结合了随机梯度下降法和顺序淘汰法，以同时利用每个系统内部的结构并进行跨系统比较。对于所提算法，我们证明了随着预算趋于无穷大，错误选择概率以指数速率收敛至零。我们进行了三个数值实验，代表了SBOS问题的实际案例。在一系列问题设置和采样预算下，与基准算法相比，我们提出的算法在错误选择概率方面表现出一致且更强的性能。
英文摘要：
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.
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。
