  Machine learning (ML) has demonstrated remarkable capabilities across many
real-world systems, from predictive modeling to intelligent automation.
However, the widespread integration of machine learning also makes it necessary
to ensure machine learning-driven decision-making systems do not violate
ethical principles and values of society in which they operate. As ML-driven
decisions proliferate, particularly in cases involving sensitive attributes
such as gender, race, and age, to name a few, the need for equity and
impartiality has emerged as a fundamental concern. In situations demanding
real-time decision-making, fairness objectives become more nuanced and complex:
instantaneous fairness to ensure equity in every time slot, and long-term
fairness to ensure fairness over a period of time. There is a growing awareness
that real-world systems that operate over long periods and require fairness
over different timelines. However, existing approaches mainly address dynamic
costs with time-invariant fairness constraints, often disregarding the
challenges posed by time-varying fairness constraints. To bridge this gap, this
work introduces a framework for ensuring long-term fairness within dynamic
decision-making systems characterized by time-varying fairness constraints. We
formulate the decision problem with fairness constraints over a period as a
constrained online optimization problem. A novel online algorithm, named
LoTFair, is presented that solves the problem 'on the fly'. We prove that
LoTFair can make overall fairness violations negligible while maintaining the
performance over the long run.
