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Byzantine machine learning has garnered considerable attention in light ofthe unpredictable faults that can occur in large-scale distributed learningsystems. The key to secure resilience against Byzantine machines in distributedlearning is resilient aggregation mechanisms. Although abundant resilientaggregation rules have been proposed, they are designed in ad-hoc manners,imposing extra barriers on comparing, analyzing, and improving the rules acrossperformance criteria. This paper studies near-optimal aggregation rules usingclustering in the presence of outliers. Our outlier-robust clustering approachutilizes geometric properties of the update vectors provided by workers. Ouranalysis show that constant approximations to the 1-center and 1-meanclustering problems with outliers provide near-optimal resilient aggregatorsfor metric-based criteria, which have been proven to be crucial in thehomogeneous and heterogeneous cases respectively. In addition, we discuss twocontradicting types of attacks under which no single aggregation rule isguaranteed to improve upon the naive average. Based on the discussion, wepropose a two-phase resilient aggregation framework. We run experiments forimage classification using a non-convex loss function. The proposed algorithmsoutperform previously known aggregation rules by a large margin with bothhomogeneous and heterogeneous data distributions among non-faulty workers. Codeand appendix are available at https://github.com/jerry907/AAAI24-RASHB.

Near-Optimal Resilient Aggregation Rules for Distributed Learning Using 1-Center and 1-Mean Clustering with Outliers