{"paper":{"title":"Breaking the $T^{3/4}$ Barrier for Regret Minimization With Bi-Dimensional CDFs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.LG","authors_text":"Alberto Marchesi, Anna Lunghi, Matteo Castiglioni","submitted_at":"2026-07-22T15:15:28Z","abstract_excerpt":"We study regret minimization for learning CDF-related objectives of the form \\[ g(x)\\cdot\\mathbb{P}_{X\\sim\\mathcal{D}}(X\\le x), \\] over $[0,1]^2$, where $g$ is a known Lipschitz function and $\\mathcal{D}$ is an unknown distribution. At each round $t$, the learner selects a point $x_t$ and observes the binary feedback $\\mathbb{I}(X_t\\le x_t)$, where $X_t\\sim\\mathcal{D}$. We design an algorithm achieving regret $\\widetilde{\\mathcal{O}}(T^{7/10})$, improving over the previous best-known bound of $\\widetilde{\\mathcal{O}}(T^{3/4})$ and showing that the curse of dimensionality can be at least partia"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.20258","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/2607.20258/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"}