multi-krum

Multi-Krum is an extension of Krum that selects the top-m most central client updates and averages them — instead of using only a single client's update (high variance), Multi-Krum selects multiple trustworthy updates and averages for lower variance while maintaining Byzantine robustness.

How Multi-Krum Works

• Score: Compute Krum scores for all clients (sum of distances to nearest neighbors).
• Select Top-m: Pick the m clients with the lowest Krum scores.
• Average: Compute the average of the m selected updates.
• m Choice: m = 1 is standard Krum. m = n - f uses all honest clients. Typical m in [f+1, n-f].

Why It Matters

• Lower Variance: Averaging multiple selected updates reduces variance compared to single-client Krum.
• Tunable: m controls the trade-off between robustness (lower m) and efficiency (higher m).
• Practical: Multi-Krum is more practical than Krum for real deployments where variance matters.

Multi-Krum is selecting the most trustworthy committee — choosing the top-m most reliable updates and averaging them for stable, robust aggregation.