  We initiate the study of the effects of non-transparency in decision rules on
individuals' ability to improve in strategic learning settings. Inspired by
real-life settings, such as loan approvals and college admissions, we remove
the assumption typically made in the strategic learning literature, that the
decision rule is fully known to individuals, and focus instead on settings
where it is inaccessible. In their lack of knowledge, individuals try to infer
this rule by learning from their peers (e.g., friends and acquaintances who
previously applied for a loan), naturally forming groups in the population,
each with possibly different type and level of information regarding the
decision rule. We show that, in equilibrium, the principal's decision rule
optimizing welfare across sub-populations may cause a strong negative
externality: the true quality of some of the groups can actually deteriorate.
On the positive side, we show that, in many natural cases, optimal improvement
can be guaranteed simultaneously for all sub-populations. We further introduce
a measure we term information overlap proxy, and demonstrate its usefulness in
characterizing the disparity in improvements across sub-populations. Finally,
we identify a natural condition under which improvement can be guaranteed for
all sub-populations while maintaining high predictive accuracy. We complement
our theoretical analysis with experiments on real-world datasets.
