Decentralized Machine Learning with Centralized Performance Guarantees via Gibbs Algorithms

Dealing simultaneously with confidentiality and Byzantine behaviors in decentralized learning is a challenging problem. Indeed, 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. While enforcing confidentiality calls for hiding the exchanged model parameters/gradients (e.g., by using cryptographic techniques), dealing with Byzantine contributions often requires inspecting the latter. Hence, most research works address these objectives separately. A recent line of work proposes to employ secure multi-party computation (MPC) to implement robust aggregators against model poisoning, thereby enforcing both confidentiality and Byzantine resilience. However, these solutions scale badly: they either require all-to-all communication between participants or delegate the entire computation to a small subset, whose computational and communication load grows proportionally with the size of the network. In this paper, we present Giskard, a protocol for confidential and Byzantine-robust decentralized aggregation. Giskard organizes $n$ parties into a tree of committees of size $O(\log n)$ and evaluates a coordinate-wise approximate median via a committee-adapted distributed binary search over the value domain, using BGW-style MPC within each committee. We assess Giskard both theoretically by proving its security and confidentiality properties and experimentally through extensive experiments involving up to one million participants. Compared to its closest competitors, Giskard reduces per-party communication complexity asymptotically while exhibiting comparable model utility under up to $n/4$ Byzantine parties.

Decentralized training is often regarded as inferior to centralized training because the consensus errors between workers are thought to undermine convergence and generalization. This work challenges this view by introducing decentralized SGD with Adaptive Consensus (DSGD-AC), which uses a time-dependent scaling mechanism to maintain consensus errors throughout the training. We show that adaptive consensus changes the stationary variance of disagreement modes by balancing two effects: it preserves consensus-error magnitude through weaker graph damping while still allowing curvature-dependent damping to shape the disagreement directions. This balance can produce a stronger Hessian-weighted loss-envelope penalty around the deployed model, even when normalized Hessian alignment is weaker than in standard DSGD. Empirical results on image classification show that DSGD-AC reaches flatter solutions and higher test accuracy than standard DSGD and even centralized SGD. Together, these results support consensus errors as a useful implicit regularizer and open a new perspective on the design of decentralized learning algorithms.

We propose a decentralized privacy-preserving learning algorithm in which each agent holds a single private sample and a shared model. Samples are learned sequentially, and each update must preserve the endpoint mappings at previously learned samples while protecting private data. This gives each agent three roles: (i) a learner that updates the model parameters, (ii) a teacher whose sample is learned at the current iteration, and (iii) a protected agent whose sample has already been learned. We build on Tuning without Forgetting (TwF) method to preserve previously learned mappings and show that TwF provides an indistinguishability guarantee for the learner whenever the set of protected agents contains another sample with the same label. For the teacher, we formulate a minimax optimal control problem that models the differential privacy noise as a worst-case disturbance to prevent performance loss while maintaining the same level of privacy for the gradient. For the protected agents, we compute the projections locally and aggregate them using a private push-sum gossip protocol. We prove geometric convergence of the decentralized gossip algorithm and of the distributed projection for TwF.