Byzantine-Robust Federated Aggregation

Aggregation Rule

Federation

Total clients 10

Malicious clients (f) 2

Attack strength 4.0×

Live Readouts

Round

Global loss

1.000

Drift from truth

0.00

Attackers filtered

0 / 0

How it works

Each of N clients holds private local data and sends only a gradient-style update vector g_i ∈ ℝ³ to the server every round — never raw data. A fraction f of clients are Byzantine: instead of an honest update they send an update scaled and flipped by the attack-strength factor, trying to drag the global model away from the true optimum.

FedAvg:   g = (1/N) Σ g_i                 (mean — one bad vector shifts it a lot)
Median:   g_k = median_i(g_i[k])          per-coordinate, k=1..3
Trimmed:  g_k = mean of the middle N-2f values of g_i[k]
Krum:     score(i) = Σ over the N-f-2 closest g_j to g_i of ||g_i-g_j||²
          pick the g_i with the smallest score

Krum and the trimmed mean are provably robust as long as f < N/2 (Krum needs 2f+2 < N): an attacker can shift a coordinate-wise mean arbitrarily by sending one huge value, but a median or a score built from nearest-neighbour distances is barely moved by a small number of outliers.

Run Round — each client computes an update toward the shared true optimum (green dot) plus noise; malicious clients replace theirs with an attack vector; the chosen rule aggregates them and the global model (white sphere) steps toward the result.
Drift from truth — Euclidean distance between the current global model and the true optimum; under FedAvg with attackers this climbs, under a robust rule it stays low.
Attackers filtered — for Krum/trimmed mean, how many of the malicious updates were excluded from the final aggregate this round.

This mirrors real defenses (Blanchard et al.'s Krum, coordinate-wise trimmed mean/median) used to keep a federated model safe when a subset of participating devices is compromised or actively poisoning training — a purely defensive statistics problem, not an attack recipe.

Honest client update Malicious client update Global model True optimum

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