  Data protection legislation like the European Union's General Data Protection
Regulation (GDPR) establishes the \textit{right to be forgotten}: a user
(client) can request contributions made using their data to be removed from
learned models. In this paper, we study how to remove the contributions made by
a client participating in a Federated Online Learning to Rank (FOLTR) system.
In a FOLTR system, a ranker is learned by aggregating local updates to the
global ranking model. Local updates are learned in an online manner at a
client-level using queries and implicit interactions that have occurred within
that specific client. By doing so, each client's local data is not shared with
other clients or with a centralised search service, while at the same time
clients can benefit from an effective global ranking model learned from
contributions of each client in the federation.
  In this paper, we study an effective and efficient unlearning method that can
remove a client's contribution without compromising the overall ranker
effectiveness and without needing to retrain the global ranker from scratch. A
key challenge is how to measure whether the model has unlearned the
contributions from the client $c^*$ that has requested removal. For this, we
instruct $c^*$ to perform a poisoning attack (add noise to this client updates)
and then we measure whether the impact of the attack is lessened when the
unlearning process has taken place. Through experiments on four datasets, we
demonstrate the effectiveness and efficiency of the unlearning strategy under
different combinations of parameter settings.
