论文标题
通过高斯流程的上下文排名和选择
Contextual Ranking and Selection with Gaussian Processes
论文作者
论文摘要
在许多现实世界中，我们面临的问题是在有限数量的替代方案中选择最好的问题，在这种替代方案中，最好的替代方法是基于上下文特定信息确定的。在这项工作中，我们研究了有限的 - 限制文本设置下的上下文排名和选择问题，我们旨在为每种上下文找到最佳替代方案。我们使用单独的高斯工艺来对每种替代方案的奖励进行建模，并为正确选择的预期和最差的上下文概率得出较大的偏差率函数。我们提出了GP-C-OCBA采样策略，该策略使用迭代分配观测值后的高斯过程以最大化速率函数。我们证明了它的一致性，并表明它在非信息性先验的假设下实现了最佳收敛率。数值实验表明，我们的算法在采样效率方面具有高度竞争力，同时具有明显较小的计算开销。
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.
