{"url":"/method/eligibility-trace","slug":"eligibility-trace","name":"Eligibility Trace","full_name":"Eligibility Trace","full_name_withheld":false,"description_markdown":"An **Eligibility Trace** is a memory vector $\\textbf{z}\\_{t} \\in \\mathbb{R}^{d}$ that parallels the long-term weight vector $\\textbf{w}\\_{t} \\in \\mathbb{R}^{d}$. The idea is that when a component of $\\textbf{w}\\_{t}$ participates in producing an estimated value, the corresponding component of $\\textbf{z}\\_{t}$ is bumped up and then begins to fade away. Learning will then occur in that component of $\\textbf{w}\\_{t}$ if a nonzero TD error occurs before the trade falls back to zero. The trace-decay parameter $\\lambda \\in \\left[0, 1\\right]$ determines the rate at which the trace falls.\r\n\r\nIntuitively, they tackle the credit assignment problem by capturing both a frequency heuristic - states that are visited more often deserve more credit - and a recency heuristic - states that are visited more recently deserve more credit.\r\n\r\n$$E\\_{0}\\left(s\\right) = 0 $$\r\n$$E\\_{t}\\left(s\\right) = \\gamma\\lambda{E}\\_{t-1}\\left(s\\right) + \\textbf{1}\\left(S\\_{t} = s\\right) $$\r\n\r\nSource: Sutton and Barto, Reinforcement Learning, 2nd Edition","description_state":"present","introduced_year":null,"introduced_by":{"title":null,"paper":null,"first_author":null,"n_authors":0,"url_abs":null,"archive_paper_url":null},"source":{"url":null,"title":null,"url_on_a_paper_host":false},"code_snippet_url":null,"code_snippet_url_on_a_code_host":false,"categories":[{"area":"Reinforcement Learning","area_id":"reinforcement-learning","collection":"Eligibility Traces","url":"/methods/category/eligibility-traces","pwc_aliases":[]}],"n_papers_tagged":11,"archive_num_papers":11,"papers_newest_first":[{"paper":null,"title":"Noise-based reward-modulated learning","date":"2025-03-31","arxiv_id":"2503.23972","n_code_links":0,"syntology":null},{"paper":null,"title":"Predecessor Features","date":"2022-06-01","arxiv_id":"2206.00303","n_code_links":0,"syntology":null},{"paper":"/paper/meta-learning-eligibility-traces-for-more","title":"META-Learning Eligibility Traces for More Sample Efficient Temporal Difference Learning","date":"2020-06-16","arxiv_id":"2006.08906","n_code_links":1,"syntology":null},{"paper":null,"title":"Efficient Use of heuristics for accelerating XCS-based Policy Learning in Markov Games","date":"2020-05-26","arxiv_id":"2005.12553","n_code_links":0,"syntology":null},{"paper":null,"title":"Gradient Q$(σ, λ)$: A Unified Algorithm with Function Approximation for Reinforcement Learning","date":"2019-09-06","arxiv_id":"1909.02877","n_code_links":0,"syntology":null},{"paper":null,"title":"Gap-Increasing Policy Evaluation for Efficient and Noise-Tolerant Reinforcement Learning","date":"2019-06-18","arxiv_id":"1906.07586","n_code_links":0,"syntology":null},{"paper":"/paper/faster-and-more-accurate-learning-with-meta","title":"META-Learning State-based Eligibility Traces for More Sample-Efficient Policy Evaluation","date":"2019-04-25","arxiv_id":"1904.11439","n_code_links":2,"syntology":{"ran":0,"of":14,"unverified":14,"pointer_only":0}},{"paper":null,"title":"Metatrace Actor-Critic: Online Step-size Tuning by Meta-gradient Descent for Reinforcement Learning Control","date":"2018-05-10","arxiv_id":"1805.04514","n_code_links":0,"syntology":null},{"paper":null,"title":"A Unified Approach for Multi-step Temporal-Difference Learning with Eligibility Traces in Reinforcement Learning","date":"2018-02-09","arxiv_id":"1802.03171","n_code_links":0,"syntology":null},{"paper":null,"title":"A forward model at Purkinje cell synapses facilitates cerebellar anticipatory control","date":"2016-12-01","arxiv_id":null,"n_code_links":0,"syntology":null},{"paper":null,"title":"Q($λ$) with Off-Policy Corrections","date":"2016-02-16","arxiv_id":"1602.04951","n_code_links":0,"syntology":null}],"papers_shown":11,"tasks":[{"task":"/task/reinforcement-learning","name":"Reinforcement Learning","papers":6},{"task":"/task/reinforcement-learning-1","name":"Reinforcement Learning (RL)","papers":6},{"task":"/task/meta-learning","name":"Meta-Learning","papers":3},{"task":"/task/reinforcement-learning-2","name":"reinforcement-learning","papers":2},{"task":"/task/atari-games","name":"Atari Games","papers":1},{"task":"/task/q-learning","name":"Q-Learning","papers":1},{"task":null,"name":"counterfactual","papers":1}],"tasks_shown":7,"n_tasks":7,"usage_by_year":[{"year":"2016","papers":2},{"year":"2018","papers":2},{"year":"2019","papers":3},{"year":"2020","papers":2},{"year":"2022","papers":1},{"year":"2025","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/eligibility-trace"},"syntology_read_at":"2026-09-24T18:15:14+00:00"}