  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.
