  We propose a generalization of the best arm identification problem in
stochastic multi-armed bandits (MAB) to the setting where every pull of an arm
is associated with delayed feedback. The delay in feedback increases the
effective sample complexity of standard algorithms, but can be offset if we
have access to partial feedback received before a pull is completed. We propose
a general framework to model the relationship between partial and delayed
feedback, and as a special case we introduce efficient algorithms for settings
where the partial feedback are biased or unbiased estimators of the delayed
feedback. Additionally, we propose a novel extension of the algorithms to the
parallel MAB setting where an agent can control a batch of arms. Our
experiments in real-world settings, involving policy search and hyperparameter
optimization in computational sustainability domains for fast charging of
batteries and wildlife corridor construction, demonstrate that exploiting the
structure of partial feedback can lead to significant improvements over
baselines in both sequential and parallel MAB.
