{"url":"/method/adasqrt","slug":"adasqrt","name":"AdaSqrt","full_name":"AdaSqrt","full_name_withheld":false,"description_markdown":"**AdaSqrt** is a stochastic optimization technique that is motivated by the observation that methods like [Adagrad](https://paperswithcode.com/method/adagrad) and [Adam](https://paperswithcode.com/method/adam) can be viewed as relaxations of [Natural Gradient Descent](https://paperswithcode.com/method/natural-gradient-descent).\r\n\r\nThe updates are performed as follows:\r\n\r\n$$ t \\leftarrow t + 1 $$\r\n\r\n$$ \\alpha\\_{t} \\leftarrow \\sqrt{t} $$\r\n\r\n$$ g\\_{t} \\leftarrow \\nabla\\_{\\theta}f\\left(\\theta\\_{t-1}\\right) $$\r\n\r\n$$ S\\_{t} \\leftarrow S\\_{t-1} + g\\_{t}^{2} $$\r\n\r\n$$ \\theta\\_{t+1} \\leftarrow \\theta\\_{t} + \\eta\\frac{\\alpha\\_{t}g\\_{t}}{S\\_{t} + \\epsilon} $$","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":"https://arxiv.org/abs/1912.09926v1","title":"Second-order Information in First-order Optimization Methods","url_on_a_paper_host":true},"code_snippet_url":null,"code_snippet_url_on_a_code_host":false,"categories":[{"area":"General","area_id":"general","collection":"Stochastic Optimization","url":"/methods/category/stochastic-optimization","pwc_aliases":[]}],"n_papers_tagged":1,"archive_num_papers":null,"papers_newest_first":[{"paper":null,"title":"Second-order Information in First-order Optimization Methods","date":"2019-12-20","arxiv_id":"1912.09926","n_code_links":0,"syntology":null}],"papers_shown":1,"tasks":[{"task":"/task/2d-human-pose-estimation","name":"2D Human Pose Estimation","papers":1}],"tasks_shown":1,"n_tasks":1,"usage_by_year":[{"year":"2019","papers":1}],"row_source":"embedded","archive":{"source":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","archive_url":"https://paperswithcode.com/method/adasqrt"},"syntology_read_at":"2026-09-24T18:15:14+00:00"}