  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.
