  This paper considers the contextual multi-armed bandit (CMAB) problem with
fairness and privacy guarantees in a federated environment. We consider
merit-based exposure as the desired fair outcome, which provides exposure to
each action in proportion to the reward associated. We model the algorithm's
effectiveness using fairness regret, which captures the difference between fair
optimal policy and the policy output by the algorithm. Applying fair CMAB
algorithm to each agent individually leads to fairness regret linear in the
number of agents. We propose that collaborative -- federated learning can be
more effective and provide the algorithm Fed-FairX-LinUCB that also ensures
differential privacy. The primary challenge in extending the existing privacy
framework is designing the communication protocol for communicating required
information across agents. A naive protocol can either lead to weaker privacy
guarantees or higher regret. We design a novel communication protocol that
allows for (i) Sub-linear theoretical bounds on fairness regret for
Fed-FairX-LinUCB and comparable bounds for the private counterpart,
Priv-FairX-LinUCB (relative to single-agent learning), (ii) Effective use of
privacy budget in Priv-FairX-LinUCB. We demonstrate the efficacy of our
proposed algorithm with extensive simulations-based experiments. We show that
both Fed-FairX-LinUCB and Priv-FairX-LinUCB achieve near-optimal fairness
regret.
