Byzantine-Robust Federated Learning is a federated learning framework designed to tolerate arbitrary malicious behavior from a fraction of participants — ensuring that the global model converges correctly even when some clients send arbitrary, adversarial gradient updates.

Byzantine Threat Model

• Byzantine Clients: Can send any gradient update — random, adversarial, or strategically crafted.
• Fraction: Typically assume $f < n/3$ or $f < n/2$ Byzantine clients (depending on the algorithm).
• Goal: The global model should converge as if the Byzantine clients didn't exist.
• No Detection: Byzantine-robust algorithms don't detect malicious clients — they ensure convergence despite them.

Why It Matters

• Multi-Party Trust: When multiple organizations collaborate, trust cannot be assumed — Byzantine robustness provides guarantees.
• Fault Tolerance: Byzantine robustness also handles faulty (non-malicious) clients with software bugs or hardware failures.
• Theory: Formal convergence guarantees under Byzantine threat models.

Byzantine-Robust FL is learning despite sabotage — provably correct federated training even when some participants are adversarial or faulty.