trimmed mean

**Trimmed Mean** is a **Byzantine-robust aggregation rule for federated learning that removes the highest and lowest values for each gradient coordinate, then averages the remaining values** — combining the robustness of the median with the efficiency of the mean. **How Trimmed Mean Works** - **For Each Coordinate**: Sort the $n$ client values for coordinate $i$. - **Trim**: Remove the $eta$ largest and $eta$ smallest values ($2eta$ total removed). - **Average**: Compute the mean of the remaining $n - 2eta$ values. - **Robustness**: Tolerates $f < eta$ Byzantine clients (their extreme values are always trimmed). **Why It Matters** - **Better Than Median**: Trimmed mean has lower variance than the median while maintaining robustness. - **Tunable**: The trimming parameter $eta$ controls the trade-off between robustness and efficiency. - **Standard**: Widely used in robust statistics and a standard baseline for robust FL aggregation. **Trimmed Mean** is **average after removing extremes** — filtering out the most suspicious gradient values for a robust yet efficient aggregation.