Modern machine learning (ML) models are capable of impressive performances. However, their prowess is not due only to the improvements in their architecture and training algorithms but also to a drastic increase in computational power used to train them. Such a drastic increase led to a growing interest in distributed ML, which in turn made worker failures and adversarial attacks an increasingly pressing concern. While distributed byzantine resilient algorithms have been proposed in a differentiable setting, none exist in a gradient-free setting. The goal of this work is to address this shortcoming. For that, we introduce a more general definition of byzantine-resilience in ML - the \textit{model-consensus}, that extends the definition of the classical distributed consensus. We then leverage this definition to show that a general class of gradient-free ML algorithms - ($1,\lambda$)-Evolutionary Search - can be combined with classical distributed consensus algorithms to generate gradient-free byzantine-resilient distributed learning algorithms. We provide proofs and pseudo-code for two specific cases - the Total Order Broadcast and proof-of-work leader election.

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