{"url":"/method/taypo","slug":"taypo","name":"TayPO","full_name":"Taylor Expansion Policy Optimization","full_name_withheld":false,"description_markdown":"**TayPO**, or **Taylor Expansion Policy Optimization**, refers to a set of algorithms that apply the $k$-th order Taylor expansions for policy optimization. This generalizes prior work, including [TRPO](https://paperswithcode.com/method/trpo) as a special case. It can be thought of unifying ideas from trust-region policy optimization and off-policy corrections. Taylor expansions share high-level similarities with both trust region policy search and off-policy corrections. To get high-level intuitions of such similarities, consider a simple 1D example of Taylor expansions. Given a sufficiently smooth real-valued function on the real line $f : \\mathbb{R} \\rightarrow \\mathbb{R}$, the $k$-th order Taylor expansion of $f\\left(x\\right)$ at $x\\_{0}$ is \r\n\r\n$$f\\_{k}\\left(x\\right) = f\\left(x\\_{0}\\right)+\\sum^{k}\\_{i=1}\\left[f^{(i)}\\left(x\\_{0}\\right)/i!\\right]\\left(x−x\\_{0}\\right)^{i}$$\r\n\r\nwhere $f^{(i)}\\left(x\\_{0}\\right)$ are the $i$-th order derivatives at $x\\_{0}$. First, a common feature shared by Taylor expansions and trust-region policy search is the inherent notion of a trust region constraint. Indeed, in order for convergence to take place, a trust-region constraint is required $|x − x\\_{0}| < R\\left(f, x\\_{0}\\right)^{1}$. Second, when using the truncation as an approximation to the original function $f\\_{K}\\left(x\\right) \\approx f\\left(x\\right)$, Taylor expansions satisfy the requirement of off-policy evaluations: evaluate target policy with behavior data. Indeed, to evaluate the truncation $f\\_{K}\\left(x\\right)$ at any $x$ (target policy), we only require the behavior policy \"data\" at $x\\_{0}$ (i.e., derivatives $f^{(i)}\\left(x\\_{0}\\right)$).","description_state":"present","introduced_year":null,"introduced_by":{"title":"Taylor Expansion Policy Optimization","paper":"/paper/taylor-expansion-policy-optimization","first_author":"Yunhao Tang","n_authors":3,"url_abs":null,"archive_paper_url":"https://paperswithcode.com/paper/taylor-expansion-policy-optimization"},"source":{"url":"https://arxiv.org/abs/2003.06259v1","title":"Taylor Expansion Policy Optimization","url_on_a_paper_host":true},"code_snippet_url":null,"code_snippet_url_on_a_code_host":false,"categories":[{"area":"Reinforcement Learning","area_id":"reinforcement-learning","collection":"Policy Gradient Methods","url":"/methods/category/policy-gradient-methods","pwc_aliases":[]}],"n_papers_tagged":1,"archive_num_papers":1,"papers_newest_first":[{"paper":"/paper/taylor-expansion-policy-optimization","title":"Taylor Expansion Policy Optimization","date":"2020-03-13","arxiv_id":"2003.06259","n_code_links":0,"syntology":null}],"papers_shown":1,"tasks":[{"task":"/task/off-policy-evaluation","name":"Off-policy evaluation","papers":1},{"task":"/task/reinforcement-learning","name":"Reinforcement Learning","papers":1},{"task":"/task/reinforcement-learning-1","name":"Reinforcement Learning (RL)","papers":1},{"task":"/task/reinforcement-learning-2","name":"reinforcement-learning","papers":1}],"tasks_shown":4,"n_tasks":4,"usage_by_year":[{"year":"2020","papers":1}],"row_source":"methods_table","archive":{"source":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","archive_url":"https://paperswithcode.com/method/taypo"},"syntology_read_at":"2026-09-24T18:15:14+00:00"}