PAC Best Arm Identification Under a Deadline
This addresses a practical challenge in scenarios like clinical trials or cloud simulations where time is constrained but sample cost matters, though it is an incremental extension of sequential best arm identification.
The paper tackles the problem of identifying an approximately optimal arm under a fixed deadline with minimal samples, introducing a setting where decisions are limited to T rounds but multiple arm pulls per round are allowed. It proposes the Elastic Batch Racing (EBR) algorithm, which is shown to be optimal and outperforms baselines by several orders of magnitude in simulations.
We study $(ε, δ)$-PAC best arm identification, where a decision-maker must identify an $ε$-optimal arm with probability at least $1 - δ$, while minimizing the number of arm pulls (samples). Most of the work on this topic is in the sequential setting, where there is no constraint on the time taken to identify such an arm; this allows the decision-maker to pull one arm at a time. In this work, the decision-maker is given a deadline of $T$ rounds, where, on each round, it can adaptively choose which arms to pull and how many times to pull them; this distinguishes the number of decisions made (i.e., time or number of rounds) from the number of samples acquired (cost). Such situations occur in clinical trials, where one may need to identify a promising treatment under a deadline while minimizing the number of test subjects, or in simulation-based studies run on the cloud, where we can elastically scale up or down the number of virtual machines to conduct as many experiments as we wish, but need to pay for the resource-time used. As the decision-maker can only make $T$ decisions, she may need to pull some arms excessively relative to a sequential algorithm in order to perform well on all possible problems. We formalize this added difficulty with two hardness results that indicate that unlike sequential settings, the ability to adapt to the problem difficulty is constrained by the finite deadline. We propose Elastic Batch Racing (EBR), a novel algorithm for this setting and bound its sample complexity, showing that EBR is optimal with respect to both hardness results. We present simulations evaluating EBR in this setting, where it outperforms baselines by several orders of magnitude.