We study exploration in stochastic multi-armed bandits when we have access to a divisible resource, and can allocate varying amounts of this resource to arm pulls. By allocating more resources to a pull, we can compute the outcome faster to inform subsequent decisions about which arms to pull. However, since distributed environments do not scale linearly, executing several arm pulls in parallel, and hence less resources per pull, may result in better throughput. For example, in simulation-based scientific studies, an expensive simulation can be sped up by running it on multiple cores. This speed-up is, however, partly offset by the communication among cores and overheads, which results in lower throughput than if fewer cores were allocated to run more trials in parallel. We explore these trade-offs in the fixed confidence setting, where we need to find the best arm with a given success probability, while minimizing the time to do so. We propose an algorithm which trades off between information accumulation and throughout and show that the time taken can be upper bounded by the solution of a dynamic program whose inputs are the squared gaps between the suboptimal and optimal arms. We prove a matching hardness result which demonstrates that the above dynamic program is fundamental to this problem. Next, we propose and analyze an algorithm for the fixed deadline setting, where we are given a time deadline and need to maximize the success probability of finding the best arm. We corroborate these theoretical insights with an empirical evaluation.

研究了在随机多臂老虎机中探索利用可分配计算资源的问题，提出了两个不同场景的算法，并验证了实验所得结论优于基准算法。

多臂赌博机探索中的资源分配：通过自适应并行处理克服亚线性缩放