Motivated by the cost heterogeneity in experimentation across different alternatives, we study the Best Arm Identification with Resource Constraints (BAIwRC) problem. The agent aims to identify the best arm under resource constraints, where resources are consumed for each arm pull. We make two novel contributions. We design and analyze the Successive Halving with Resource Rationing algorithm (SH-RR). The SH-RR achieves a near-optimal non-asymptotic rate of convergence in terms of the probability of successively identifying an optimal arm. Interestingly, we identify a difference in convergence rates between the cases of deterministic and stochastic resource consumption.

翻译：受实验过程中不同备选方案成本差异的驱动，我们研究了资源受限下的最佳臂识别（BAIwRC）问题。智能体需要在资源约束条件下识别最佳臂，其中每次拉臂操作均会消耗资源。本文做出两项创新贡献：设计并分析了资源配给下的逐次淘汰算法（SH-RR）。该算法在成功识别最优臂的概率方面，实现了近乎最优的非渐近收敛速率。值得注意的是，我们发现了确定性资源消耗与随机性资源消耗两种情形下收敛速率的差异性。