{"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/guarantees-for-tuning-the-step-size-using-a","title":"Guarantees for Tuning the Step Size using a Learning-to-Learn Approach","arxiv_id":"2006.16495","date":"2020-06-30","proceeding":null,"authors":["Xiang Wang","Shuai Yuan","Chenwei Wu","Rong Ge"],"abstract":"Choosing the right parameters for optimization algorithms is often the key to their success in practice. Solving this problem using a learning-to-learn approach -- using meta-gradient descent on a meta-objective based on the trajectory that the optimizer generates -- was recently shown to be effective. However, the meta-optimization problem is difficult. In particular, the meta-gradient can often explode/vanish, and the learned optimizer may not have good generalization performance if the meta-objective is not chosen carefully. In this paper we give meta-optimization guarantees for the learning-to-learn approach on a simple problem of tuning the step size for quadratic loss. Our results show that the na\\\"ive objective suffers from meta-gradient explosion/vanishing problem. Although there is a way to design the meta-objective so that the meta-gradient remains polynomially bounded, computing the meta-gradient directly using backpropagation leads to numerical issues. We also characterize when it is necessary to compute the meta-objective on a separate validation set to ensure the generalization performance of the learned optimizer. Finally, we verify our results empirically and show that a similar phenomenon appears even for more complicated learned optimizers parametrized by neural networks.","url_abs":"https://arxiv.org/abs/2006.16495v2","url_pdf":"https://arxiv.org/pdf/2006.16495v2.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":"guarantees-for-tuning-the-step-size-using-a","repo_url":"https://github.com/Kolin96/learning-to-learn","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"tf","reach":{"status":"ok","spdx":"MIT"}}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=2006.16495","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"2006.16495"}},"developers":"https://syntology.ai/developers","read_at":"2026-09-24T18:15:14+00:00","read_at_is":"when the build read Syntology's graph, not when any sample ran","claim":"Per-sample execution status on synthesized fixtures; not a correctness claim about the paper. 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