We consider the continuum-armed bandits problem, under a novel setting of recommending the best arms within a fixed budget under aggregated feedback. This is motivated by applications where the precise rewards are impossible or expensive to obtain, while an aggregated reward or feedback, such as the average over a subset, is available. We constrain the set of reward functions by assuming that they are from a Gaussian Process and propose the Gaussian Process Optimistic Optimisation (GPOO) algorithm. We adaptively construct a tree with nodes as subsets of the arm space, where the feedback is the aggregated reward of representatives of a node. We propose a new simple regret notion with respect to aggregated feedback on the recommended arms. We provide theoretical analysis for the proposed algorithm, and recover single point feedback as a special case. We illustrate GPOO and compare it with related algorithms on simulated data.

提出了用高斯过程进行连续赌博机问题的最优解优化算法，适用于在固定预算下推荐最佳赌博机并获取平均回报。在提供集合平均值等聚合反馈而精确奖励成本较高或不可能时使用，通过高斯过程约束奖励函数集合，并在节点之间自适应构建树状结构。

带汇总反馈的高斯过程赌博机