{"paper":{"title":"Online Learning Quantum States with the Logarithmic Loss via VB-FTRL","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG","math.OC","stat.ML"],"primary_cat":"quant-ph","authors_text":"Kai-Chun Chen, Wei-Fu Tseng, Yen-Huan Li, Zi-Hong Xiao","submitted_at":"2023-11-06T15:45:33Z","abstract_excerpt":"Online learning of quantum states with the logarithmic loss (LL-OLQS) is a quantum generalization of online portfolio selection (OPS), a classic open problem in online learning for over three decades. This problem also emerges in designing stochastic optimization algorithms for maximum-likelihood quantum state tomography. Recently, Jezequel et al. (arXiv:2209.13932) proposed the VB-FTRL algorithm, the first regret-optimal algorithm for OPS with moderate computational complexity. In this paper, we generalize VB-FTRL for LL-OLQS. Let $d$ denote the dimension and $T$ the number of rounds. The gen"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2311.04237","kind":"arxiv","version":3},"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/2311.04237/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"}