{"id":"palomar/PALOMAR-2026-09-10-000003","url":"https://github.com/Arthur742Ramos/blackwell-approachability-lean/tree/8a53170bbf91309d687d4f0131b2147457a3dbc3","json":"https://data.palomar-registry.org/entries/PALOMAR-2026-09-10-000003-v1.json","repo":"https://github.com/Arthur742Ramos/blackwell-approachability-lean","tags":["cs.GT","cs.LG","msc:91A26","msc:68T05","game-theory","phi-regret","online-learning","lean"],"score":0,"title":"Irreducible improper phi-regret in Lean","trust":"high","domain":"cs.GT","source":"palomar","authors":["Arthur Freitas Ramos"],"reviews":0,"subject":"cs.GT","summary":"A Mathlib-only formalization of two explicit three-action improper phi-regret families in Section 4.4.1 of Dann, Mansour, Mohri, Schneider, and Sivan (COLT 2025). They are finite counterexample families for the paper's rate-preserving linear-reduction program. It proves valid-improper certificates, the affine-hyperplane invariant-transport core of Lemma 4, the extreme-point antipodal-displacement core of Lemma 5, a direct finite one-way affine action/loss-transfer-to-canonical bridge, a source-style two-direction affine linear-equivalence-to-canonical bridge in an explicit…","category":"research","comments":0,"disputed":false,"division":"cs","mentions":0,"verified":true,"discussed":0,"published":"2026-09-10","reactions":{},"formalized":true,"formalizes":[{"title":"Rate-Preserving Reductions for Blackwell Approachability","identifier":"https://proceedings.mlr.press/v291/dann25a.html","relationship":"formalizes"}]}