Uncovering the Connection Between Differential Privacy and Certified Robustness of Federated Learning against Poisoning Attacks

Federated learning (FL) provides an efficient paradigm to jointly train a global model leveraging data from distributed users. As the local training data come from different users who may not be trustworthy, several studies have shown that FL is vulnerable to poisoning attacks. Meanwhile, to protect the privacy of local users, FL is always trained in a differentially private way (DPFL). Thus, in this paper, we ask: Can we leverage the innate privacy property of DPFL to provide certified robustness against poisoning attacks? Can we further improve the privacy of FL to improve such certification? We first investigate both user-level and instance-level privacy of FL and propose novel mechanisms to achieve improved instance-level privacy. We then provide two robustness certification criteria: certified prediction and certified attack cost for DPFL on both levels. Theoretically, we prove the certified robustness of DPFL under a bounded number of adversarial users or instances. Empirically, we conduct extensive experiments to verify our theories under a range of attacks on different datasets. We show that DPFL with a tighter privacy guarantee always provides stronger robustness certification in terms of certified attack cost, but the optimal certified prediction is achieved under a proper balance between privacy protection and utility loss.