Satisficing in Gaussian bandit problems

We propose a satisficing objective for the multi-armed bandit problem, i.e., where the objective is to achieve performance above a given threshold. We show that this new problem is equivalent to a standard multi-armed bandit problem with a maximizing objective and use this equivalence to find bounds on performance in terms of the satisficing objective. For the special case of Gaussian rewards we show that the satisficing problem is equivalent to a related standard multi-armed bandit problem again with Gaussian rewards. We apply the Upper Credible Limit (UCL) algorithm to this standard problem and show how it achieves optimal performance in terms of the satisficing objective.