Pith Number

pith:77GGG73V

pith:2026:77GGG73V3X7Z5PCAFAIKNPRBS6

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A Diagnostic Framework for Implementation Risk in Bilevel Decision Problems: The Ambiguity Premium and the Robustness--Efficiency Frontier

Jiguang Yu

Bilevel decisions carry hidden implementation risk when follower responses are near-optimal rather than exactly optimal.

arxiv:2605.16780 v1 · 2026-05-16 · math.OC

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Claims

C1strongest 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.

C2weakest 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.

C3one 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.

References

91 extracted · 91 resolved · 4 Pith anchors

[1] An overview of bilevel optimization 2007

[2] Bidi- rectional endothelial feedback drives turing-vascular patterning and drug-resistance niches: a hybrid pde-agent-based study.Bioengineering, 12(10):1097, 2025 2025

[3] Algebraic–spectral thresholds and discrete–continuous stability transfer in leslie–gower systems.Electronic Research Archive, 34(1):251–290, 2026 2026

[4] Analysis and mean-field limit of a hybrid pde-abm modeling angiogenesis-regulated resistance evolution.Mathematics, 13(17):2898, 2025 2025

[5] Stephan Dempe.Foundations of bilevel programming. Springer, 2002. 21 2002

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Receipt and verification

First computed	2026-05-20T00:03:21.624424Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ffcc637f75ddff9ebc402810a6be2197b9f752557c5633985776b741239443be

Aliases

arxiv: 2605.16780 · arxiv_version: 2605.16780v1 · doi: 10.48550/arxiv.2605.16780 · pith_short_12: 77GGG73V3X7Z · pith_short_16: 77GGG73V3X7Z5PCA · pith_short_8: 77GGG73V

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/77GGG73V3X7Z5PCAFAIKNPRBS6 \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: ffcc637f75ddff9ebc402810a6be2197b9f752557c5633985776b741239443be

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0c2d691e007fbc03c3908ceae3204158598adfdca742cb68e1e5ab03e2b577d2",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.OC",
    "submitted_at": "2026-05-16T03:20:37Z",
    "title_canon_sha256": "9704b6a819d8b0878611e4c55a2f1776fc6fea55327d78fdade8b6b2de3d913a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.16780",
    "kind": "arxiv",
    "version": 1
  }
}