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 $\beta$ largest and $\beta$ smallest values ($2\beta$ total removed).
• Average: Compute the mean of the remaining $n - 2\beta$ values.
• Robustness: Tolerates $f < \beta$ 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 $\beta$ 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.