  We study federated unlearning, a novel problem to eliminate the impact of
specific clients or data points on the global model learned via federated
learning (FL). This problem is driven by the right to be forgotten and the
privacy challenges in FL. We introduce a new framework for exact federated
unlearning that meets two essential criteria: \textit{communication efficiency}
and \textit{exact unlearning provability}. To our knowledge, this is the first
work to tackle both aspects coherently. We start by giving a rigorous
definition of \textit{exact} federated unlearning, which guarantees that the
unlearned model is statistically indistinguishable from the one trained without
the deleted data. We then pinpoint the key property that enables fast exact
federated unlearning: total variation (TV) stability, which measures the
sensitivity of the model parameters to slight changes in the dataset.
Leveraging this insight, we develop a TV-stable FL algorithm called
\texttt{FATS}, which modifies the classical
\texttt{\underline{F}ed\underline{A}vg} algorithm for \underline{T}V
\underline{S}tability and employs local SGD with periodic averaging to lower
the communication round. We also design efficient unlearning algorithms for
\texttt{FATS} under two settings: client-level and sample-level unlearning. We
provide theoretical guarantees for our learning and unlearning algorithms,
proving that they achieve exact federated unlearning with reasonable
convergence rates for both the original and unlearned models. We empirically
validate our framework on 6 benchmark datasets, and show its superiority over
state-of-the-art methods in terms of accuracy, communication cost, computation
cost, and unlearning efficacy.
