  We consider the optimization problem of the form $\min_{x \in \mathbb{R}^d}
f(x) \triangleq \mathbb{E}_{\xi} [F(x; \xi)]$, where the component $F(x;\xi)$
is $L$-mean-squared Lipschitz but possibly nonconvex and nonsmooth. The
recently proposed gradient-free method requires at most $\mathcal{O}( L^4
d^{3/2} \epsilon^{-4} + \Delta L^3 d^{3/2} \delta^{-1} \epsilon^{-4})$
stochastic zeroth-order oracle complexity to find a
$(\delta,\epsilon)$-Goldstein stationary point of objective function, where
$\Delta = f(x_0) - \inf_{x \in \mathbb{R}^d} f(x)$ and $x_0$ is the initial
point of the algorithm. This paper proposes a more efficient algorithm using
stochastic recursive gradient estimators, which improves the complexity to
$\mathcal{O}(L^3 d^{3/2} \epsilon^{-3}+ \Delta L^2 d^{3/2} \delta^{-1}
\epsilon^{-3})$.
