  Equipping current decision-making tools with notions of fairness,
equitability, or other ethically motivated outcomes, is one of the top
priorities in recent research efforts in machine learning, AI, and
optimization. In this paper, we investigate how to allocate limited resources
to {locally interacting} communities in a way to maximize a pertinent notion of
equitability. In particular, we look at the dynamic setting where the
allocation is repeated across multiple periods (e.g., yearly), the local
communities evolve in the meantime (driven by the provided allocation), and the
allocations are modulated by feedback coming from the communities themselves.
We employ recent mathematical tools stemming from data-driven feedback online
optimization, by which communities can learn their (possibly unknown)
evolution, satisfaction, as well as they can share information with the
deciding bodies. We design dynamic policies that converge to an allocation that
maximize equitability in the long term. We further demonstrate our model and
methodology with realistic examples of healthcare and education subsidies
design in Sub-Saharian countries. One of the key empirical takeaways from our
setting is that long-term equitability is fragile, in the sense that it can be
easily lost when deciding bodies weigh in other factors (e.g., equality in
allocation) in the allocation strategy. Moreover, a naive compromise, while not
providing significant advantage to the communities, can promote inequality in
social outcomes.
