{"paper":{"title":"Accelerated Methods for Riemannian Min-Max Optimization Ensuring Bounded Geometric Penalties","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG"],"primary_cat":"math.OC","authors_text":"Christopher Criscitiello, Christophe Roux, David Mart\\'inez-Rubio, Sebastian Pokutta","submitted_at":"2023-05-25T15:43:07Z","abstract_excerpt":"In this work, we study optimization problems of the form $\\min_x \\max_y f(x, y)$, where $f(x, y)$ is defined on a product Riemannian manifold $\\mathcal{M} \\times \\mathcal{N}$ and is $\\mu_x$-strongly geodesically convex (g-convex) in $x$ and $\\mu_y$-strongly g-concave in $y$, for $\\mu_x, \\mu_y \\geq 0$. We design accelerated methods when $f$ is $(L_x, L_y, L_{xy})$-smooth and $\\mathcal{M}$, $\\mathcal{N}$ are Hadamard. To that aim we introduce new g-convex optimization results, of independent interest: we show global linear convergence for metric-projected Riemannian gradient descent and improve "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2305.16186","kind":"arxiv","version":2},"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/2305.16186/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"}