Giskard : Byzantine Robust and Private Aggregation for Large-Scale Decentralized Learning

Abstract

In decentralized learning, clients train a machine learning model while keeping their data locally and share their model parameters or gradients with a set of neighbors, making it vulnerable to both privacy attacks and model poisoning attacks. Jointly addressing privacy and Byzantine behavior in decentralized learning is challenging. Indeed, Differential Privacy (DP) applied on the client side is known to increase the variance of honest model updates, which weakens Byzantine-robust aggregation against poisoning attacks. Distributed DP can mitigate this issue by adding noise after aggregation, but implementing it without a trusted curator requires both confidential and Byzantine-resilient computation. Recent work addresses this challenge using secure multi-party computation (MPC) to implement robust aggregation while preserving input confidentiality. However, these solutions scale badly: they either require all-to-all communication between participants or delegate the entire computation to a small subset of parties whose computational and communication cost grows with network size. In this paper, we present Giskard, a scalable protocol for private and Byzantine-robust decentralized aggregation. Giskard organizes $n$ parties into a tree of committees of size $O(\log n)$ and evaluates a differentially private coordinate-wise approximate median via a committee-adapted secure quantile search over the value domain, using MPC within each committee. We assess Giskard both theoretically by proving its security and privacy properties and empirically through extensive experiments involving up to one million participants. Compared to its closest competitors, Giskard reduces per-party communication complexity by close to three orders of magnitude over the closest competitor while exhibiting comparable robustness under up to $n/4$ Byzantine parties.