  An unbiased low-variance gradient estimator, termed GO gradient, was proposed
recently for expectation-based objectives
$\mathbb{E}_{q_{\boldsymbol{\gamma}}(\boldsymbol{y})} [f(\boldsymbol{y})]$,
where the random variable (RV) $\boldsymbol{y}$ may be drawn from a stochastic
computation graph with continuous (non-reparameterizable) internal nodes and
continuous/discrete leaves. Upgrading the GO gradient, we present for
$\mathbb{E}_{q_{\boldsymbol{\boldsymbol{\gamma}}}(\boldsymbol{y})}
[f(\boldsymbol{y})]$ an unbiased low-variance Hessian estimator, named GO
Hessian. Considering practical implementation, we reveal that GO Hessian is
easy-to-use with auto-differentiation and Hessian-vector products, enabling
efficient cheap exploitation of curvature information over stochastic
computation graphs. As representative examples, we present the GO Hessian for
non-reparameterizable gamma and negative binomial RVs/nodes. Based on the GO
Hessian, we design a new second-order method for
$\mathbb{E}_{q_{\boldsymbol{\boldsymbol{\gamma}}}(\boldsymbol{y})}
[f(\boldsymbol{y})]$, with rigorous experiments conducted to verify its
effectiveness and efficiency.
