  The stochastic multi-armed bandit problem is a well-known model for studying
the exploration-exploitation trade-off. It has significant possible
applications in adaptive clinical trials, which allow for dynamic changes in
the treatment allocation probabilities of patients. However, most bandit
learning algorithms are designed with the goal of minimizing the expected
regret. While this approach is useful in many areas, in clinical trials, it can
be sensitive to outlier data, especially when the sample size is small. In this
paper, we define and study a new robustness criterion for bandit problems.
Specifically, we consider optimizing a function of the distribution of returns
as a regret measure. This provides practitioners more flexibility to define an
appropriate regret measure. The learning algorithm we propose to solve this
type of problem is a modification of the BESA algorithm [Baransi et al., 2014],
which considers a more general version of regret. We present a regret bound for
our approach and evaluate it empirically both on synthetic problems as well as
on a dataset from the clinical trial literature. Our approach compares
favorably to a suite of standard bandit algorithms.
