A Non-asymptotic Approach to Best-Arm Identification for Gaussian Bandits
This addresses the challenge of efficiently identifying the best arm in multi-armed bandit settings, offering a more stable and interpretable algorithm for applications like clinical trials or recommendation systems, though it is an incremental improvement over existing methods.
The paper tackles the problem of best-arm identification in Gaussian bandits by proposing Exploration-Biased Sampling, which achieves non-asymptotic bounds that asymptotically match optimal sample complexity while improving stability and interpretability through a bias toward exploration.
We propose a new strategy for best-arm identification with fixed confidence of Gaussian variables with bounded means and unit variance. This strategy, called Exploration-Biased Sampling, is not only asymptotically optimal: it is to the best of our knowledge the first strategy with non-asymptotic bounds that asymptotically matches the sample complexity.But the main advantage over other algorithms like Track-and-Stop is an improved behavior regarding exploration: Exploration-Biased Sampling is biased towards exploration in a subtle but natural way that makes it more stable and interpretable. These improvements are allowed by a new analysis of the sample complexity optimization problem, which yields a faster numerical resolution scheme and several quantitative regularity results that we believe of high independent interest.