Before revision:  Furthermore, we show that the minimax optimality does not come at the price of overly aggressive experimentation as we provide upper bounds on the expected number of times any suboptimal treatment is assigned. We also consider the case where the outcome of a treatment is only observed with delay as it may take time for the treatment to work. Thus, a doctor faces a tradeoff between getting imprecise information quickly by making the measurement soon after the treatment is given or getting precise information later at the expense of less information for the individuals who are treated in the meantime .
After revision:  Furthermore, we show that the minimax optimality does not come at the price of overly aggressive experimentation as we provide upper bounds on the expected number of suboptimal treatments only grows slowly in the number of treatments .