Contextual Ranking and Selection with Gaussian Processes and Optimal Computing Budget Allocation
研究在有限备选方案和有限上下文下，如何为每个上下文找到最佳方案，提出GP-C-OCBA采样策略，利用高斯过程后验迭代分配观测以最大化正确选择的概率，并证明其一致性和最优收敛速度。
In many real-world problems, we are faced with the problem of selecting the best among a finite number of alternatives, where the best alternative is determined based on context specific information. In this work, we study the contextual Ranking and Selection problem under a finite-alternative-finite-context setting, where we aim to find the best alternative for each context. We use a separate Gaussian process to model the reward for each alternative and derive the large deviations rate function for both the expected and worst-case contextual probability of correct selection. We propose the GP-C-OCBA sampling policy, which uses the Gaussian process posterior to iteratively allocate observations to maximize the rate function. We prove its consistency and show that it achieves the optimal convergence rate under the assumption of a non-informative prior. Numerical experiments show that our algorithm is highly competitive in terms of sampling efficiency, while having significantly smaller computational overhead.