Pith Number

pith:73DHL43M

pith:2026:73DHL43MTQGSOFFAAGSK3DCNSA

not attested not anchored not stored refs resolved

Min-Max Optimization Requires Exponentially Many Queries

Alexandros Hollender, Andrea Celli, Martino Bernasconi, Matteo Castiglioni

Any algorithm finding an ε-approximate stationary point in nonconvex-nonconcave min-max optimization requires exponentially many queries.

arxiv:2605.13806 v1 · 2026-05-13 · cs.DS · cs.CC · cs.GT · cs.LG · math.OC

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Record completeness

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2 Internet Archive

3 Author claim open · sign in to claim

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

any algorithm that finds an ε-approximate stationary point must make a number of queries that is exponential in 1/ε or d

C2weakest assumption

The function belongs to the nonconvex-nonconcave class and the oracle model provides exact access to f and ∇f; if the class is restricted further or oracles are noisy, the exponential bound may not apply.

C3one line summary

Finding an ε-approximate stationary point for nonconvex-nonconcave min-max optimization over [0,1]^d × [0,1]^d requires exponentially many queries in 1/ε or d.

References

6 extracted · 6 resolved · 0 Pith anchors

[1] A polynomial-time algorithm for variational inequalities under the Minty condition 1983

[2] On the Role of Constraints in the Complexity of Min-Max Optimization 2024

[3] Pure- Circuit: Tight Inapproximability for PPAD 2024

[4] Playing large games using simple strategies 2003

[5] Cycles in adversarial regularized learning 2018

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-18T02:44:15.446729Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

fec675f36c9c0d2714a001a4ad8c4d900764362d180c56ecafbed3485decb26d

Aliases

arxiv: 2605.13806 · arxiv_version: 2605.13806v1 · doi: 10.48550/arxiv.2605.13806 · pith_short_12: 73DHL43MTQGS · pith_short_16: 73DHL43MTQGSOFFA · pith_short_8: 73DHL43M

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/73DHL43MTQGSOFFAAGSK3DCNSA \
  | 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: fec675f36c9c0d2714a001a4ad8c4d900764362d180c56ecafbed3485decb26d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "14e8bc0b758d6a616f7e79f8ec5f6c8f633cf6edd69ba18f67fbc11e948a2104",
    "cross_cats_sorted": [
      "cs.CC",
      "cs.GT",
      "cs.LG",
      "math.OC"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.DS",
    "submitted_at": "2026-05-13T17:34:24Z",
    "title_canon_sha256": "2ef13c8da93afdcabee2615e62d100e3b8e2793b8c0d107cda5c89b227dd56f4"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.13806",
    "kind": "arxiv",
    "version": 1
  }
}