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.