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                <term xml:lang="en"> bandit problem</term>
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              <p>This manuscript  deals with the  estimation of the  optimal rule and  its meanreward in a simple bandit setting where,  at each round, the player is given acontext,  chooses  one of  two  actions  based on  the  context  and all  pastobservations, and  receives a reward  corresponding to the  action undertaken.The  player focuses  on the  mean reward  and tries  to narrow  her confidenceinterval for  it, but it happens  that she can also  estimate her regret.Inference hinges  on the  targeted learning  methodology.  A  simulation studyillustrates the results of the manuscript.</p>
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