  Monotone inclusions have a wide range of applications, including
minimization, saddle-point, and equilibria problems. We introduce new
stochastic algorithms, with or without variance reduction, to estimate a root
of the expectation of possibly set-valued monotone operators, using at every
iteration one call to the resolvent of a randomly sampled operator. We also
introduce a notion of similarity between the operators, which holds even for
discontinuous operators. We leverage it to derive linear convergence results in
the strongly monotone setting.
