Pith Number

pith:3XULHAME

pith:2025:3XULHAMED7DXR53QKACTU4A6JF

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A Scenario Approach to the Robustness of Nonconvex-Nonconcave Minimax Problems

Guanpu Chen, Huan Peng, Karl Henrik Johansson

The scenario approach yields a probabilistic robustness guarantee for ε-stationary points in nonconvex-nonconcave minimax problems by proving monotonicity of the stationary residual.

arxiv:2511.15606 v2 · 2025-11-19 · cs.GT · math.OC

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4 Citations open

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The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Claims

C1strongest claim

we first establish a probabilistic robustness guarantee for an ε-stationary point, overcoming the dependence on the non-degeneracy assumption by proving the monotonicity of the stationary residual in the number of scenarios.

C2weakest assumption

Convex strategy sets for all players together with the standard assumptions of the scenario optimization framework from prior literature.

C3one line summary

Scenario approach establishes probabilistic robustness for epsilon-stationary points in convex-strategy minimax problems via monotonicity of residuals and a relaxed bound for global points in nonconvex cases.

References

3 extracted · 3 resolved · 0 Pith anchors

[1] Aliprantis, C.D. and Border, K.C. (2006). Inﬁnite Dimen- sional Analysis: A Hitchhiker’s Guide . Springer, 3rd edition. Assif, M., Chatterjee, D., and Banavar, R. (2020). Scenario approach for minmax 2006 · doi:10.1109/tac.2025.3634219

[2] Goodfellow, I., Pouget-Abadie, J., Mirza, M., Xu, B., Warde-Farley, D., Ozair, S., Courville, A., and Bengio, Y. (2014). Generative adversarial nets. In Advances in Neural Information Processing Syste 2014

[3] Yang, J., Orvieto, A., Lucchi, A., and He, N. (2022). Faster single-loop algorithms for minimax optimization without strong concavity. In International Conference on Artiﬁcial Intelligence and Statist 2022

Receipt and verification

First computed	2026-05-18T03:09:33.196177Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

dde8b381841fc778f77050053a701e494a47b5c0145fd795cef991f12a02af33

Aliases

arxiv: 2511.15606 · arxiv_version: 2511.15606v2 · doi: 10.48550/arxiv.2511.15606 · pith_short_12: 3XULHAMED7DX · pith_short_16: 3XULHAMED7DXR53Q · pith_short_8: 3XULHAME

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/3XULHAMED7DXR53QKACTU4A6JF \
  | 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: dde8b381841fc778f77050053a701e494a47b5c0145fd795cef991f12a02af33

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a826d1f49940b00c68106b9ab83ec1c3c310a2447357b54f7640366ee1201b05",
    "cross_cats_sorted": [
      "math.OC"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.GT",
    "submitted_at": "2025-11-19T16:53:29Z",
    "title_canon_sha256": "b10dcbdd3f43f186243d07d5fe0db04a01fe9e5bb2a88dbce35e847846a39a24"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2511.15606",
    "kind": "arxiv",
    "version": 2
  }
}