{"paper":{"title":"Trade-off Functions for DP-SGD with Subsampling based on Random Shuffling: Tight Upper and Lower Bounds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"DP-SGD with random shuffling subsampling yields tight closed-form trade-off function bounds that converge to the ideal 1-a diagonal under suitable epoch scaling.","cross_cats":["cs.CR"],"primary_cat":"cs.LG","authors_text":"Marten van Dijk, Murat Bilgehan Ertan","submitted_at":"2026-05-07T13:35:43Z","abstract_excerpt":"We derive a tight analysis of the trade-off function for Differentially Private Stochastic Gradient Descent (DP-SGD) with subsampling based on random shuffling within the $f$-DP framework. Our analysis covers the regime $\\sigma \\geq \\sqrt{3/\\ln M}$, where $\\sigma$ is the noise multiplier and $M$ is the number of rounds within a single epoch. Unlike $f$-DP analyses for Poisson subsampling, which yield non-closed implicit formulas that can be machine computed but are non-transparent, random shuffling admits a tight analysis yielding transparent and interpretable closed-form bounds. Our concrete "},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"Our analysis covers the regime σ ≥ √(3/ln M) ... yielding transparent and interpretable closed-form bounds. ... if E=c_M²M with c_M→0, then the E-fold composed trade-off function satisfies f⊗E(a)→1-a uniformly in a∈[0,1] with δ having only an O(√E) dependency.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The central claims rest on the regime restriction σ ≥ √(3/ln M) together with the applicability of the Berry-Esseen theorem to the relevant sum of bounded random variables arising from the shuffling process; if this concentration regime does not hold or the approximation error exceeds the claimed tightness, the explicit bounds and the uniform convergence to the diagonal fail.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Tight closed-form bounds via Berry-Esseen show DP-SGD with random shuffling achieves near-ideal privacy (trade-off close to 1-a) for σ ≥ √(3/ln M) and large M, with δ linear in epochs restricting E to O(√M) and an asymptotic O(√E) δ under E = c_M²M.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"DP-SGD with random shuffling subsampling yields tight closed-form trade-off function bounds that converge to the ideal 1-a diagonal under suitable epoch scaling.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"05373b1745876bfc152e5d1b8f98ac8ba461ac56a936ea15ed26bac697f20351"},"source":{"id":"2605.06259","kind":"arxiv","version":2},"verdict":{"id":"6245de5c-8528-47c4-848b-ddba4edb08c8","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-08T13:18:54.489496Z","strongest_claim":"Our analysis covers the regime σ ≥ √(3/ln M) ... yielding transparent and interpretable closed-form bounds. ... if E=c_M²M with c_M→0, then the E-fold composed trade-off function satisfies f⊗E(a)→1-a uniformly in a∈[0,1] with δ having only an O(√E) dependency.","one_line_summary":"Tight closed-form bounds via Berry-Esseen show DP-SGD with random shuffling achieves near-ideal privacy (trade-off close to 1-a) for σ ≥ √(3/ln M) and large M, with δ linear in epochs restricting E to O(√M) and an asymptotic O(√E) δ under E = c_M²M.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The central claims rest on the regime restriction σ ≥ √(3/ln M) together with the applicability of the Berry-Esseen theorem to the relevant sum of bounded random variables arising from the shuffling process; if this concentration regime does not hold or the approximation error exceeds the claimed tightness, the explicit bounds and the uniform convergence to the diagonal fail.","pith_extraction_headline":"DP-SGD with random shuffling subsampling yields tight closed-form trade-off function bounds that converge to the ideal 1-a diagonal under suitable epoch scaling."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.06259/integrity.json","findings":[],"available":true,"detectors_run":[{"name":"claim_evidence","ran_at":"2026-05-20T12:42:04.136767Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"ai_meta_artifact","ran_at":"2026-05-20T08:34:32.783202Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"doi_title_agreement","ran_at":"2026-05-19T18:31:19.641768Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"doi_compliance","ran_at":"2026-05-19T12:50:31.043554Z","status":"completed","version":"1.0.0","findings_count":0}],"snapshot_sha256":"1faf0048ad26d5bcbf1471d97ce972bfbab94a13cd7e647471c41db0328bf131"},"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"}