  We develop two novel stochastic variance-reduction methods to approximate a
solution of root-finding problems applicable to both equations and inclusions.
Our algorithms leverage a new combination of ideas from the
forward-reflected-backward splitting method and a class of unbiased
variance-reduction estimators. We construct two new stochastic estimators
within this class, inspired by the well-established SVRG and SAGA estimators.
These estimators differ significantly from existing approaches used for
root-finding algorithms. By appropriately selecting parameters, both algorithms
achieve the state-of-the-art oracle complexity of $\mathcal{O}(n + n^{2/3}
\epsilon^{-2})$ for achieving an $\epsilon$-solution in terms of the operator
residual norm, where $n$ represents the number of summands and $\epsilon$
signifies the desired accuracy. This complexity aligns with the best-known
results in stochastic nonconvex optimization without enhancements. We test our
algorithms on two numerical examples and compare them with existing methods.
The results demonstrate promising improvements offered by the new methods
compared to their competitors.
