{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/go-hessian-for-expectation-based-objectives","title":"GO Hessian for Expectation-Based Objectives","arxiv_id":"2006.08873","date":"2020-06-16","proceeding":null,"authors":["Yulai Cong","Miaoyun Zhao","Jianqiao Li","Junya Chen","Lawrence Carin"],"abstract":"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.","url_abs":"https://arxiv.org/abs/2006.08873v1","url_pdf":"https://arxiv.org/pdf/2006.08873v1.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"abstracts"},"code_links":[{"paper_slug":"go-hessian-for-expectation-based-objectives","repo_url":"https://github.com/YulaiCong/GOHessian","is_official":1,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"pytorch","reach":{"status":"ok","spdx":"MIT"}}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}