# Rigorous Systems Research Group (RSRG) Seminar

Thursday, January 24, 2019
12:00pm to 1:00pm
Annenberg 213
We assume in each communication round, up to $q$ ($q \not=0$) out of the $m$ workers suffer Byzantine faults. Each worker keeps a local sample of size $n$ (which can possibly be small) and the total sample size is $N=nm$. We propose two secured variants of the gradient descent method with different robust gradient aggregation rules.
The first variant is based on the simple geometric median of means.  We show that the estimation error converges to $O(\sqrt{qd/N})$, where $d$ is the model dimension.
The second variant is based on an iterative filtering procedure. We show that the estimation error converges to $O(\sqrt{q/N} + \sqrt{d/N})$. As long as $q=O(d)$, our proposed algorithm achieves the optimal error rate $O(\sqrt{d/N})$ in the fault-free environments.