{"paper":{"title":"Quantum Speedups of Optimizing Approximately Convex Functions with Applications to Logarithmic Regret Stochastic Convex Bandits","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.LG","math.OC"],"primary_cat":"quant-ph","authors_text":"Ruizhe Zhang, Tongyang Li","submitted_at":"2022-09-26T03:19:40Z","abstract_excerpt":"We initiate the study of quantum algorithms for optimizing approximately convex functions. Given a convex set ${\\cal K}\\subseteq\\mathbb{R}^{n}$ and a function $F\\colon\\mathbb{R}^{n}\\to\\mathbb{R}$ such that there exists a convex function $f\\colon\\mathcal{K}\\to\\mathbb{R}$ satisfying $\\sup_{x\\in{\\cal K}}|F(x)-f(x)|\\leq \\epsilon/n$, our quantum algorithm finds an $x^{*}\\in{\\cal K}$ such that $F(x^{*})-\\min_{x\\in{\\cal K}} F(x)\\leq\\epsilon$ using $\\tilde{O}(n^{3})$ quantum evaluation queries to $F$. This achieves a polynomial quantum speedup compared to the best-known classical algorithms. As an app"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2209.12897","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2209.12897/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}