  Subset selection tasks, arise in recommendation systems and search engines
and ask to select a subset of items that maximize the value for the user. The
values of subsets often display diminishing returns, and hence, submodular
functions have been used to model them. If the inputs defining the submodular
function are known, then existing algorithms can be used. In many applications,
however, inputs have been observed to have social biases that reduce the
utility of the output subset. Hence, interventions to improve the utility are
desired. Prior works focus on maximizing linear functions -- a special case of
submodular functions -- and show that fairness constraint-based interventions
can not only ensure proportional representation but also achieve near-optimal
utility in the presence of biases. We study the maximization of a family of
submodular functions that capture functions arising in the aforementioned
applications. Our first result is that, unlike linear functions,
constraint-based interventions cannot guarantee any constant fraction of the
optimal utility for this family of submodular functions. Our second result is
an algorithm for submodular maximization. The algorithm provably outputs
subsets that have near-optimal utility for this family under mild assumptions
and that proportionally represent items from each group. In empirical
evaluation, with both synthetic and real-world data, we observe that this
algorithm improves the utility of the output subset for this family of
submodular functions over baselines.

Machine Learning;Artificial Intelligence;Computers and Society;Information Retrieval;Machine Learning