Quantile Multi-Armed Bandits with 1-bit Feedback
This work addresses risk-sensitive decision-making under communication constraints, which is incremental as it builds on best-arm identification by incorporating quantile rewards and limited feedback.
The paper tackles the problem of identifying the arm with the highest quantile reward in a multi-armed bandit setting with 1-bit feedback per arm pull, proposing an algorithm that achieves sample complexity upper bounds matching lower bounds to within logarithmic or constant factors under certain conditions.
In this paper, we study a variant of best-arm identification involving elements of risk sensitivity and communication constraints. Specifically, the goal of the learner is to identify the arm with the highest quantile reward, while the communication from an agent (who observes rewards) and the learner (who chooses actions) is restricted to only one bit of feedback per arm pull. We propose an algorithm that utilizes noisy binary search as a subroutine, allowing the learner to estimate quantile rewards through 1-bit feedback. We derive an instance-dependent upper bound on the sample complexity of our algorithm and provide an algorithm-independent lower bound for specific instances, with the two matching to within logarithmic factors under mild conditions, or even to within constant factors in certain low error probability scaling regimes. The lower bound is applicable even in the absence of communication constraints, and thus we conclude that restricting to 1-bit feedback has a minimal impact on the scaling of the sample complexity.