Fair Algorithms for Learning in Allocation Problems
Hadi Elzayn, Shahin Jabbari, Christopher Jung, Michael Kearns, Seth Neel, Aaron Roth, Zachary Schutzman
Settings such as lending and policing
can be modeled by a centralized agent allocating a scarce
resource (e.g. loans or police officers) amongst several groups,
in order to maximize some objective (e.g. loans given that are repaid, or
criminals that are apprehended).
Often in such problems fairness is also a concern. One natural
notion of fairness, based on general principles of equality of opportunity,
asks that conditional on an individual being a candidate for the
resource in question, the probability of actually receiving it is approximately independent
of the individual's group. For example, in lending this would mean that equally
creditworthy individuals in different racial groups have roughly equal chances of
receiving a loan. In policing it would mean that two individuals committing the same
crime in different districts would have roughly equal chances of being arrested.
In this paper we formalize this general notion of fairness for allocation problems,
and investigate its algorithmic consequences. Our main technical results
include an efficient learning algorithm that converges to an optimal fair allocation
even when the allocator does not know the frequency of candidates
(i.e. creditworthy individuals or criminals) in each group. This algorithm operates in a
censored feedback model in which only the number of candidates who received the resource in a
given allocation can be observed, rather than the true number of candidates in each group. This
models the fact that we do not learn the creditworthiness of individuals we do not give loans to,
and do not learn about crimes committed if the police presence in a district is low.
As an application of our framework and algorithm,
we consider the predictive policing problem, in which the resource being
allocated to each group is the number of police officers assigned to each district.
The learning algorithm is trained on arrest
data gathered from its own deployments on previous days,
resulting in a potential feedback loop that our algorithm provably overcomes.
In this case, the fairness constraint asks that
the probability that an individual who has committed a crime
is arrested should be independent of the district in which they live.
We empirically investigate the performance of our learning algorithm on the Philadelphia Crime Incidents dataset.