论文标题
为基于期望的目标去黑森州
GO Hessian for Expectation-Based Objectives
论文作者
论文摘要
最近，提出了一个公正的低相位梯度估计器，称为GO梯度，是针对基于期望的目标$ \ MATHBB {e} _ {q _ {q _ {\boldsymbolγ}（\ boldsymbol {y}）} [f（\ boldsymbol {y}）$，wern y Miay $，the y Mouniabl $ ther从具有连续（不可逆转）内部节点和连续/离散叶的随机计算图。升级GO梯度，我们以$ \ mathbb {e} _ {q _ {\ boldsymbol {\boldsymbolγ}}}}}}}}（\ boldsymbol {y}）} [f（\ boldsymbol {y}）] $无数低相位估算的nessian nisian。考虑到实际的实施，我们透露，Go Hessian易于使用自动差异和Hessian-vector产品，从而可以通过随机计算图有效地对曲率信息进行有效的廉价开发。作为代表性的示例，我们提出了不可逆转伽马和负二项式RVS/节点的Go Hessian。基于Go Hessian，我们为$ \ Mathbb {e} _ {q _ {\ boldsymbol {\BoldSymbolγ}}（\ BoldSymbol {y}）}} [F（\ BoldSymbol {Y}）$，具有严格的验证效率的效率和效率。
An unbiased low-variance gradient estimator, termed GO gradient, was proposed recently for expectation-based objectives $\mathbb{E}_{q_{\boldsymbolγ}(\boldsymbol{y})} [f(\boldsymbol{y})]$, 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 $\mathbb{E}_{q_{\boldsymbol{\boldsymbolγ}}(\boldsymbol{y})} [f(\boldsymbol{y})]$ 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 $\mathbb{E}_{q_{\boldsymbol{\boldsymbolγ}}(\boldsymbol{y})} [f(\boldsymbol{y})]$, with rigorous experiments conducted to verify its effectiveness and efficiency.
