Federated learning involves a group of workers and a central server to train a machine learning model in a distributed manner. However, the distributed structure poses challenges in terms of communication efficiency and robustness against malicious attacks. Our work assumes the presence of Byzantine attackers among workers and considers Byzantine robustness in federated learning. In order to overcome the challenges of communication and Byzantine attacks, we propose a novel method called Byzantine-robust compressed and momentum-based variance reduction (BR-CoMVaR). This method innovatively combines Byzantine-robustness aggregation, gradient difference compression, and momentum-based variance reduction. Gradient difference compression helps to mitigate the effect of compression noise, while momentum-based variance reduction reduces the variance in local stochastic gradients and accelerates convergence. The incorporation of these two techniques with Byzantine-robustness aggregation further enhances the defense capability against Byzantine attacks and improves overall Byzantine robustness. Moreover, the extensive experimental results display the superior performance of BR-CoMVaR compared with other three most related algorithms.

Blind super-resolution can be cast as a low rank matrix recovery problem by exploiting the inherent simplicity of the signal. In this paper, we develop a simple yet efficient non-convex method for this problem based on the low rank structure of the vectorized Hankel matrix associated with the target matrix. Theoretical guarantees have been established under the similar conditions as convex approaches. Numerical experiments are also conducted to demonstrate its performance.

We consider the problem of resolving$r$point sources from$n$samples at the low end of the spectrum when point spread functions (PSFs) are not known. Assuming that the spectrum samples of the PSFs lie in low dimensional subspace (let$s$denote the dimension), we can formulate it as a matrix recovery problem, followed by location estimation. By exploiting the low rank structure of the vectorized Hankel matrix associated with the target matrix, a convex approach called Vectorized Hankel Lift is proposed for the matrix recovery. It is shown that$n\gtrsim rs\log ^{4} n$samples are sufficient for Vectorized Hankel Lift to achieve the exact recovery. For the location retrieval from the matrix, applying the single snapshot MUSIC method within the vectorized Hankel lift framework corresponds to the spatial smoothing technique proposed to improve the performance of the MMV MUSIC for the direction-of-arrival (DOA) estimation.