{"paper":{"title":"Geometry-Aware Multi-Armed Bandits for Antenna Beam Selection on Spheres, Tori, $\\SO(3)$, and Reconfigurable Intelligent Surfaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"Intrinsic Matérn kernels on spheres, tori and discrete tori cut cumulative regret in mmWave beam selection by 25 to 45 percent versus standard codebook methods.","cross_cats":[],"primary_cat":"eess.SP","authors_text":"Changsheng Chen, Ning Xie, Yuriy Dorn","submitted_at":"2026-05-13T04:59:38Z","abstract_excerpt":"Beam alignment in mmWave phased arrays and RIS-assisted links is a stochastic bandit under both short TTI budgets and Doppler-induced non-stationarity. The arm space is a Riemannian manifold: $\\sphere^2$ for steering, $\\torus^n$ for phase combining, $\\SO(3)$ for panel orientation, or the discrete torus $(\\mathbb Z_B)^M$ with up to $K\\!\\sim\\!10^{90}$ configurations for $B$-level RIS ($B\\!=\\!2^b$, $b$ bits/element); the intrinsic Mat\\'ern kernel of Borovitskiy et al.\\ provides the base GP. We contribute two algorithmic pieces. \\textbf{(C1)} A Kronecker-factorised intrinsic-product Mat\\'ern kerne"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"On four static 3GPP-style mmWave benchmarks, intrinsic-kernel GP-UCB reduces cumulative regret by 25–45% vs. codebook UCB1/Thompson and by 10–33% vs. Euclidean-ambient GP-UCB on the toroidal arm spaces; AdaptiveGP-v2 is statistically indistinguishable from the hand-tuned fixed-window oracle at every speed.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"That the intrinsic Matérn kernel from Borovitskiy et al. accurately captures the reward landscape on these manifolds and that per-sample marginal likelihood selection of window size W remains stable and unbiased under the non-stationarity induced by Doppler.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"A Kronecker-factorized intrinsic Matérn kernel renders GP-UCB tractable on RIS spaces with up to 10^90 configurations while an online marginal-likelihood adaptive window controller matches hand-tuned performance across speeds without per-deployment calibration.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Intrinsic Matérn kernels on spheres, tori and discrete tori cut cumulative regret in mmWave beam selection by 25 to 45 percent versus standard codebook methods.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"3366cf44ae49ea54b968e288ee8ec0cfcdfbff29d003fe8daee3318576566bee"},"source":{"id":"2605.13005","kind":"arxiv","version":1},"verdict":{"id":"5ed48f10-1a7c-45ac-9e57-2d39655a17a3","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-14T18:46:36.941790Z","strongest_claim":"On four static 3GPP-style mmWave benchmarks, intrinsic-kernel GP-UCB reduces cumulative regret by 25–45% vs. codebook UCB1/Thompson and by 10–33% vs. Euclidean-ambient GP-UCB on the toroidal arm spaces; AdaptiveGP-v2 is statistically indistinguishable from the hand-tuned fixed-window oracle at every speed.","one_line_summary":"A Kronecker-factorized intrinsic Matérn kernel renders GP-UCB tractable on RIS spaces with up to 10^90 configurations while an online marginal-likelihood adaptive window controller matches hand-tuned performance across speeds without per-deployment calibration.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"That the intrinsic Matérn kernel from Borovitskiy et al. accurately captures the reward landscape on these manifolds and that per-sample marginal likelihood selection of window size W remains stable and unbiased under the non-stationarity induced by Doppler.","pith_extraction_headline":"Intrinsic Matérn kernels on spheres, tori and discrete tori cut cumulative regret in mmWave beam selection by 25 to 45 percent versus standard codebook methods."},"references":{"count":36,"sample":[{"doi":"","year":2026,"title":"RISA: Simulated annealing-based algorithm for RIS adjustment in time-varying channels,","work_id":"a4da1a87-6f32-4ee3-9a89-6b776fd290e1","ref_index":1,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2022,"title":"Conditional-sample-mean bandits for fast beam training in reconfigurable intelligent surfaces,","work_id":"dc461cdc-4f8f-4a38-bc20-d4a3a3c11230","ref_index":2,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2024,"title":"Model-free optimization and experimental validation of RIS-assisted wireless communications under rich multipath fading,","work_id":"95aa4828-23fd-4cd6-b033-4ce08c6dddf8","ref_index":3,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2008,"title":"Multi-armed bandits in metric spaces,","work_id":"05fbf330-006a-4348-8bba-ad8653ac8d0f","ref_index":4,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2011,"title":"X-armed bandits","work_id":"2c8b9584-c53c-45aa-9857-9e77684cd781","ref_index":5,"cited_arxiv_id":"","is_internal_anchor":false}],"resolved_work":36,"snapshot_sha256":"45bdbc72a84f1c62aea77499a3e39bb1993e42602e9e7bf4103c1bbb9d481cc0","internal_anchors":0},"formal_canon":{"evidence_count":2,"snapshot_sha256":"a191c5a8053e8fb5631ff3e5fe70481dcd45c5c80016ea6209bfb7c0ebfe93ad"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}