  We investigate and provide new insights on the sampling rule called Top-Two
Thompson Sampling (TTTS). In particular, we justify its use for
fixed-confidence best-arm identification. We further propose a variant of TTTS
called Top-Two Transportation Cost (T3C), which disposes of the computational
burden of TTTS. As our main contribution, we provide the first sample
complexity analysis of TTTS and T3C when coupled with a very natural Bayesian
stopping rule, for bandits with Gaussian rewards, solving one of the open
questions raised by Russo (2016). We also provide new posterior convergence
results for TTTS under two models that are commonly used in practice: bandits
with Gaussian and Bernoulli rewards and conjugate priors.
