{"paper":{"title":"A Diagnostic Framework for Implementation Risk in Bilevel Decision Problems: The Ambiguity Premium and the Robustness--Efficiency Frontier","license":"http://creativecommons.org/licenses/by/4.0/","headline":"Bilevel decisions carry hidden implementation risk when follower responses are near-optimal rather than exactly optimal.","cross_cats":[],"primary_cat":"math.OC","authors_text":"Jiguang Yu","submitted_at":"2026-05-16T03:20:37Z","abstract_excerpt":"Hierarchical decision problems are often modeled as bilevel programs in which a leader commits to a policy and a follower responds optimally. When the follower's optimal response is nonunique, or when only near-optimal follower behavior can be verified, the same leader decision may induce a range of upper-level outcomes. This paper develops a diagnostic framework for quantifying that exposure. For a leader decision $x$, we evaluate the optimistic and pessimistic upper-level values over the $\\epsilon$-optimal follower response set $S_\\epsilon(x)$ and use their difference, \\[\n  \\Delta_\\epsilon(x"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"We establish a diameter bound Δ_ε(x) ≤ L_F(x) diam(S_ε(x)) and an O(√ε) estimate under quadratic lower-level growth. The contribution here is to make it operational as an implementation-risk diagnostic.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The lower-level problem satisfies a quadratic growth condition (or at least local Lipschitz continuity of the upper-level value function) that allows the O(√ε) rate and the diameter bound to hold; this is invoked to derive the estimates for the ambiguity premium.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"The paper defines the ambiguity premium Δ_ε(x) as the gap between pessimistic and optimistic upper-level values over ε-optimal follower responses and provides bounds plus a screening workflow to trace robustness-efficiency frontiers in bilevel problems.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Bilevel decisions carry hidden implementation risk when follower responses are near-optimal rather than exactly optimal.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"79baf4f82c736d91bfd2edb96a7ab82d09db8c0617fb3d52f7ec70d2ab656b55"},"source":{"id":"2605.16780","kind":"arxiv","version":1},"verdict":{"id":"da7edcc7-4a4b-4f78-b0b5-ec8a97f8dc28","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-19T21:19:17.810027Z","strongest_claim":"We establish a diameter bound Δ_ε(x) ≤ L_F(x) diam(S_ε(x)) and an O(√ε) estimate under quadratic lower-level growth. The contribution here is to make it operational as an implementation-risk diagnostic.","one_line_summary":"The paper defines the ambiguity premium Δ_ε(x) as the gap between pessimistic and optimistic upper-level values over ε-optimal follower responses and provides bounds plus a screening workflow to trace robustness-efficiency frontiers in bilevel problems.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The lower-level problem satisfies a quadratic growth condition (or at least local Lipschitz continuity of the upper-level value function) that allows the O(√ε) rate and the diameter bound to hold; this is invoked to derive the estimates for the ambiguity premium.","pith_extraction_headline":"Bilevel decisions carry hidden implementation risk when follower responses are near-optimal rather than exactly optimal."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.16780/integrity.json","findings":[],"available":true,"detectors_run":[{"name":"doi_title_agreement","ran_at":"2026-05-19T21:31:19.345398Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"doi_compliance","ran_at":"2026-05-19T21:31:00.966806Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"claim_evidence","ran_at":"2026-05-19T19:01:56.303021Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"ai_meta_artifact","ran_at":"2026-05-19T18:33:26.438462Z","status":"skipped","version":"1.0.0","findings_count":0}],"snapshot_sha256":"90fbb5e28daf8620920a308fb297985d3fbb7992ecd84c5379401f2984b9e92d"},"references":{"count":91,"sample":[{"doi":"","year":2007,"title":"An overview of bilevel optimization","work_id":"d86ad406-bf2f-4780-9e18-327743c0c66b","ref_index":1,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2025,"title":"Bidi- rectional endothelial feedback drives turing-vascular patterning and drug-resistance niches: a hybrid pde-agent-based study.Bioengineering, 12(10):1097, 2025","work_id":"79618f5a-ae19-4632-be28-6bc54d3c1e5c","ref_index":2,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2026,"title":"Algebraic–spectral thresholds and discrete–continuous stability transfer in leslie–gower systems.Electronic Research Archive, 34(1):251–290, 2026","work_id":"ac11df8d-4b5b-4fce-bafe-7eae94c07afd","ref_index":3,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2025,"title":"Analysis and mean-field limit of a hybrid pde-abm modeling angiogenesis-regulated resistance evolution.Mathematics, 13(17):2898, 2025","work_id":"7fa1a3cb-ce77-45af-aa60-60f53ece9d69","ref_index":4,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2002,"title":"Stephan Dempe.Foundations of bilevel programming. 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