Byzantine-Robust Decentralized Learning via Remove-then-Clip Aggregation

We consider decentralized learning over a network of workers with heterogeneous datasets, in the presence of Byzantine workers. Byzantine workers may transmit arbitrary or malicious values to neighboring workers, leading to degradation in overall performance. The heterogeneous nature of the training data across various workers complicates the identification and mitigation of Byzantine workers. To address this complex problem, we introduce a resilient decentralized learning approach that combines the gradient descent algorithm with a novel robust aggregator. Specifically, we propose a remove-then-clip aggregator, whereby each benign worker meticulously filters the neighbors' values and subsequently projects the remaining values to a sphere centered at its local value, with an appropriately selected radius. We prove that our proposed method converges to a neighborhood of a stationary point for non-convex objectives under standard assumptions. Furthermore, empirical evaluations are provided to demonstrate the superior performance of our method in comparison to existing algorithms, under various Byzantine attack models.