This paper studies the Byzantine Agreement problem where the nodes have access to a predictor that flags nodes for suspicion of faulty (Byzantine) behavior. We focus on algorithmic resilience -- the maximum number of faulty nodes an algorithm can tolerate -- and present algorithms and impossibility results whose resilience depend on the accuracy of the predictor. As our first main result, we bring a complete characterization of the consistency--robustness trade-offs in both the non-authenticated and authenticated settings: for n nodes and a parameter α∈[0,1], we present algorithms that tolerate up to α⋅n faulty nodes when the predictor is correct (consistency), and up to 21−α⋅n−1 faulty nodes when the predictor is arbitrarily wrong (robustness); in the authenticated setting the robustness bound improves to (1−α)⋅n−1. These trade-offs are exactly tight as we show that one additional faulty node renders the problem impossible. Our second main result characterizes smoothness: the rate at which resilience degrades as the predictor becomes less accurate. We show that resilience linearly decreases in the number of wrong predictions as long as that number stays within a constant fraction of n. Concretely, in the non-authenticated setting each additional wrong prediction loses one unit of resilience, whereas in the authenticated setting the decline is halved since two wrong predictions are needed to lose one unit of resilience.
Byzantine-robust aggregation rules such as multi-Krum assume a central coordinator, and decentralising them is obstructed by the rules themselves: they are globally coupled, non-associative, and discontinuous, so an ulpscale perturbation can flip the selected subset, moving the output by a non-vanishing amount. None of this prevents coordinator-free replication, because a robust rule needs no agreed order of contributions, only an agreed set and an agreed exclusion predicate, both of which converge without consensus. ACFA (Accountable Consensus-Free Aggregation) replicates a content-addressed OR-Set of signed contributions and a grow-only set of self-authenticating equivocation proofs, offline-verifiable by anyone. Aggregation is a deterministic pure function of the converged product state: fixed-point integer arithmetic over a hash-canonical order, ties broken by content hash. We prove that any pure function of a converged product of CRDTs (non-monotone, non-associative, or stochastic) inherits Strong Eventual Consistency, together with its converse; the contribution is the composition of a data lattice with an evidence lattice applied to a robust selector, not the elementary lifting step. A prototype (10 nodes, 3 Byzantine) passes 16/16 falsification checks: byte-identical roots under adversarial gossip, deterministic re-convergence after late equivocation proofs, partition recovery, and three byte-identity-breaking ablations. The guarantee is consistency, not accuracy; robustness is imported, conditional on 2f + 3 admitted contributions (at most f Byzantine) and a stated quantisation-margin condition.
We study distributed Byzantine-resilient actor-critic multi-agent reinforcement learning (AC-MARL), where agents collectively learn policies through local interactions. Existing methods guarantee convergence of the agents' parameters only to a neighborhood of the attack-free limit points, resulting in degraded performance. We propose Fully Resilient AC-MARL (FRAC-MARL), a decentralized method in which each agent leverages redundancy in two-hop messages to identify reliable messages. Under linear parameterizations of the value and team-reward functions and Byzantine edge attacks, where adversarial behavior is confined to the communication layer, we prove that agents' parameters converge almost surely to the same limit points as in the attack-free case over time-varying communication graphs. We introduce a novel topological condition for the convergence of our method, present a systematic method to construct such networks, and prove that this condition can be verified in polynomial time. Finally, we demonstrate our method on cooperative multi-robot formation control tasks.
We investigate robust federated learning, where a group of workers collaboratively train a shared model under the orchestration of a central server in the presence of Byzantine adversaries capable of arbitrary and potentially malicious behaviors. To simultaneously enhance communication efficiency and resilience against such adversaries, we propose a Byzantine-resilient Nesterov-accelerated federated learning (Byrd-NAFL) algorithm. Byrd-NAFL seamlessly integrates Nesterov's momentum into the federated learning process alongside Byzantine-resilient aggregation rules to achieve fast and safe convergence against gradient corruption. We establish a finite-time convergence guarantee for Byrd-NAFL under non-convex and smooth loss functions with relaxed assumptions on the aggregated gradients. Extensive numerical experiments validate the effectiveness of Byrd-NAFL and demonstrate the superiority over existing benchmarks in terms of convergence speed, accuracy, and resilience to diverse malicious attacks.