{"url":"/method/expected-sarsa","slug":"expected-sarsa","name":"Expected Sarsa","full_name":"Expected Sarsa","full_name_withheld":false,"description_markdown":"**Expected Sarsa** is like [Q-learning](https://paperswithcode.com/method/q-learning) but instead of taking the maximum over next state-action pairs, we use the expected value, taking into account how likely each action is under the current policy.\r\n\r\n$$Q\\left(S\\_{t}, A\\_{t}\\right) \\leftarrow Q\\left(S\\_{t}, A\\_{t}\\right) + \\alpha\\left[R_{t+1} + \\gamma\\sum\\_{a}\\pi\\left(a\\mid{S\\_{t+1}}\\right)Q\\left(S\\_{t+1}, a\\right) - Q\\left(S\\_{t}, A\\_{t}\\right)\\right] $$\r\n\r\nExcept for this change to the update rule, the algorithm otherwise follows the scheme of Q-learning. It is more computationally expensive than [Sarsa](https://paperswithcode.com/method/sarsa) but it eliminates the variance due to the random selection of $A\\_{t+1}$.\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":"Off-Policy TD Control","url":"/methods/category/off-policy-td-control","pwc_aliases":[]},{"area":"Reinforcement Learning","area_id":"reinforcement-learning","collection":"On-Policy TD Control","url":"/methods/category/on-policy-td-control","pwc_aliases":[]}],"n_papers_tagged":9,"archive_num_papers":9,"papers_newest_first":[{"paper":null,"title":"Reinforcement Learning for Hanabi","date":"2025-05-31","arxiv_id":"2506.00458","n_code_links":0,"syntology":null},{"paper":null,"title":"Convergent NMPC-based Reinforcement Learning Using Deep Expected Sarsa and Nonlinear Temporal Difference Learning","date":"2025-02-07","arxiv_id":"2502.04925","n_code_links":0,"syntology":null},{"paper":"/paper/solving-royal-game-of-ur-using-reinforcement","title":"Solving Royal Game of Ur Using Reinforcement Learning","date":"2022-08-23","arxiv_id":"2208.10669","n_code_links":2,"syntology":null},{"paper":null,"title":"On the Convergence of SARSA with Linear Function Approximation","date":"2022-02-14","arxiv_id":"2202.06828","n_code_links":0,"syntology":null},{"paper":null,"title":"A study of first-passage time minimization via Q-learning in heated gridworlds","date":"2021-10-05","arxiv_id":"2110.02129","n_code_links":0,"syntology":null},{"paper":null,"title":"Chrome Dino Run using Reinforcement Learning","date":"2020-08-15","arxiv_id":"2008.06799","n_code_links":0,"syntology":null},{"paper":null,"title":"Model-free Reinforcement Learning for Stochastic Stackelberg Security Games","date":"2020-05-24","arxiv_id":"2005.11853","n_code_links":0,"syntology":null},{"paper":null,"title":"The Concept of Criticality in Reinforcement Learning","date":"2018-10-16","arxiv_id":"1810.07254","n_code_links":0,"syntology":null},{"paper":null,"title":"Multi-step Reinforcement Learning: A Unifying Algorithm","date":"2017-03-03","arxiv_id":"1703.01327","n_code_links":0,"syntology":null}],"papers_shown":9,"tasks":[{"task":"/task/reinforcement-learning-1","name":"Reinforcement Learning (RL)","papers":8},{"task":"/task/reinforcement-learning-2","name":"reinforcement-learning","papers":7},{"task":"/task/reinforcement-learning","name":"Reinforcement Learning","papers":6},{"task":"/task/q-learning","name":"Q-Learning","papers":4},{"task":"/task/board-games","name":"Board Games","papers":1},{"task":"/task/card-games","name":"Card Games","papers":1},{"task":"/task/deep-reinforcement-learning","name":"Deep Reinforcement Learning","papers":1}],"tasks_shown":7,"n_tasks":7,"usage_by_year":[{"year":"2017","papers":1},{"year":"2018","papers":1},{"year":"2020","papers":2},{"year":"2021","papers":1},{"year":"2022","papers":2},{"year":"2025","papers":2}],"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/expected-sarsa"},"syntology_read_at":"2026-09-24T18:15:14+00:00"}