  Thompson sampling has impressive empirical performance for many multi-armed
bandit problems. But current algorithms for Thompson sampling only work for the
case of conjugate priors since these algorithms require to infer the posterior,
which is often computationally intractable when the prior is not conjugate. In
this paper, we propose a novel algorithm for Thompson sampling which only
requires to draw samples from a tractable distribution, so our algorithm is
efficient even when the prior is non-conjugate. To do this, we reformulate
Thompson sampling as an optimization problem via the Gumbel-Max trick. After
that we construct a set of random variables and our goal is to identify the one
with highest mean. Finally, we solve it with techniques in best arm
identification.
