Unified Breakdown Analysis for Byzantine Robust Gossip

In decentralized machine learning, different de-vices communicate in a peer-to-peer manner to collaboratively learn from each other's data. Such approaches are vulnerable to misbehaving (or Byzantine) devices. We introduce F-RG, a gen-eral framework for building robust decentralized algorithms with guarantees arising from robust-sum-like aggregation rules F. We then investigate the notion of breakdown point, and show an upper bound on the number of adversaries that decen-tralized algorithms can tolerate. We introduce a practical robust aggregation rule, coined CS+, such that CS+-RG has a near-optimal breakdown. Other choices of aggregation rules lead to existing algorithms such as ClippedGossip or NNA. We give experimental evidence to validate the effec-tiveness of CS+-RG and highlight the gap with NNA, in particular against a novel attack tailored to decentralized communications.