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For deterministic bilevel optimization, we provide a comprehensive convergence rate analysis for two popular algorithms respectively based on approximate implicit differentiation (AID) and iterative differentiation (ITD). For the AID-based method, we orderwisely improve the previous convergence rate analysis due to a more practical parameter selection as well as a warm start strategy, and for the ITD-based method we establish the first theoretical convergence rate. Our analysis also provides a quantitative comparison between ITD and AID based approaches. For stochastic bilevel optimization, we propose a novel algorithm named stocBiO, which features a sample-efficient hypergradient estimator using efficient Jacobian- and Hessian-vector product computations. We provide the convergence rate guarantee for stocBiO, and show that stocBiO outperforms the best known computational complexities orderwisely with respect to the condition number $\\kappa$ and the target accuracy $\\epsilon$. We further validate our theoretical results and demonstrate the efficiency of bilevel optimization algorithms by the experiments on meta-learning and hyperparameter optimization.","url_abs":"https://arxiv.org/abs/2010.07962v3","url_pdf":"https://arxiv.org/pdf/2010.07962v3.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":"provably-faster-algorithms-for-bilevel-1","repo_url":"https://github.com/junjieyang97/stocbio_hp","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"pytorch","reach":{"status":"ok","spdx":"MIT"}},{"paper_slug":"provably-faster-algorithms-for-bilevel-1","repo_url":"https://github.com/JunjieYang97/stocBiO","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"pytorch","reach":null}],"tasks":[{"task_slug":"bilevel-optimization","task_name":"Bilevel Optimization"},{"task_slug":"hyperparameter-optimization","task_name":"Hyperparameter Optimization"},{"task_slug":"meta-learning","task_name":"Meta-Learning"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=2010.07962","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"2010.07962"}},"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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