GO Hessian for Expectation-Based Objectives

An unbiased low-variance gradient estimator, termed GO gradient, was proposed recently for expectation-based objectives E_q_γ(y) [f(y)], where the random variable (RV) y may be drawn from a stochastic computation graph (SCG) with continuous (non-reparameterizable) internal nodes and continuous/discrete leaves. Based on we present [f(y)] an Hessian named Hessian, which contains deterministic as special case. Considering practical implementation, reveal that in expectation obeys chain rule is therefore easy-to-use auto-differentiation Hessian-vector products, enabling efficient cheap exploitation of curvature information over deep SCGs. As representative examples, non-reparameterizable gamma negative binomial RVs/nodes. Leveraging develop new second-order method challenging experiments conducted to verify its effectiveness efficiency.