  In this paper, we consider a best action identification problem in the
stochastic linear bandit setup with a fixed confident constraint. In the
considered best action identification problem, instead of minimizing the
accumulative regret as done in existing works, the learner aims to obtain an
accurate estimate of the underlying parameter based on his action and reward
sequences. To improve the estimation efficiency, the learner is allowed to
select his action based his historical information; hence the whole procedure
is designed in a sequential adaptive manner. We first show that the existing
algorithms designed to minimize the accumulative regret is not a consistent
estimator and hence is not a good policy for our problem. We then characterize
a lower bound on the estimation error for any policy. We further design a
simple policy and show that the estimation error of the designed policy
achieves the same scaling order as that of the derived lower bound.
