{"paper":{"title":"Instance-Optimal Matrix Multiplicative Weight Update and Its Quantum Applications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.AI","cs.DS","quant-ph","stat.ML"],"primary_cat":"cs.LG","authors_text":"Tongyang Li, Weiyuan Gong, Xinzhao Wang, Zhiyu Zhang","submitted_at":"2025-09-10T18:15:41Z","abstract_excerpt":"The Matrix Multiplicative Weight Update (MMWU) is a seminal online learning algorithm with numerous applications. Applied to the matrix version of the Learning from Expert Advice (LEA) problem on the $d$-dimensional spectraplex, it is well known that MMWU achieves the minimax-optimal regret bound of $O(\\sqrt{T\\log d})$, where $T$ is the time horizon. In this paper, we present an improved algorithm achieving the instance-optimal regret bound of $O(\\sqrt{T\\cdot S(X||d^{-1}I_d)})$, where $X$ is the comparator in the regret, $I_d$ is the identity matrix, and $S(\\cdot||\\cdot)$ denotes the quantum r"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2509.08911","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/2509.08911/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"}