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pith:7PBBOKTZ

pith:2026:7PBBOKTZPXTU6HEZLUCKYIMYWL

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Deep Policy Iteration for High-Dimensional Mean-Field Games with Regenerative Reformulation

Hui Zhang, Shuixin Fang, Shupeng Wang, Tao Zhou, Zhen Wu

By reformulating mean-field games into regenerative problems with deterministic cycles, deep policy iteration becomes efficient and scalable in dimensions up to 10,000.

arxiv:2604.26782 v2 · 2026-04-29 · math.NA · cs.NA

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Claims

C1strongest claim

The resulting method is efficient and scalable in high dimensions, as it avoids the direct solution of the coupled Hamilton-Jacobi-Bellman and Fokker-Planck system, the full simulation of trajectories to estimate the population measure, the explicit computation of conditional expectations in policy evaluation, and pointwise optimization in policy improvement. Numerical experiments demonstrate that the proposed method effectively handles dimensions up to 10,000.

C2weakest assumption

The mean-field game can be reformulated as a regenerative problem with deterministic cycles such that policy evaluation, policy improvement, and population measure estimation can be accurately performed cycle by cycle using particle approximations updated via one-step random mappings from Euler-Maruyama discretization.

C3one line summary

A deep policy iteration method reformulates finite-horizon mean-field games as regenerative problems with deterministic cycles, using particle systems and one-step updates to handle dimensions up to 10,000 efficiently.

References

54 extracted · 54 resolved · 0 Pith anchors

[1] Mean field games for modeling crowd motion 2019

[2] Extensions of the deep Galerkin method.Appl 2022

[3] A maximum principle for SDEs of mean-field type.Appl 2011

[4] SpringerBriefs in Mathematics 2013

[5] Mean field control and mean field game models with several populations.Minimax Theory Appl., 3(2):173–209, 2018 2018

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-20T00:00:39.755670Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

fbc2172a797de74f1c995d04ac2198b2c16171cfbe052e927399565f2559cf46

Aliases

arxiv: 2604.26782 · arxiv_version: 2604.26782v2 · doi: 10.48550/arxiv.2604.26782 · pith_short_12: 7PBBOKTZPXTU · pith_short_16: 7PBBOKTZPXTU6HEZ · pith_short_8: 7PBBOKTZ

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/7PBBOKTZPXTU6HEZLUCKYIMYWL \
  | 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: fbc2172a797de74f1c995d04ac2198b2c16171cfbe052e927399565f2559cf46

Canonical record JSON

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    "abstract_canon_sha256": "9a462aea1012266cdf571736ed3fbc3f1a766c755e7eee7b4d73b106e4c23d0e",
    "cross_cats_sorted": [
      "cs.NA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NA",
    "submitted_at": "2026-04-29T15:13:23Z",
    "title_canon_sha256": "df71af87e72d2025923ba0672ee4b86635162aaaf94ca29b95bcb3bae9dfe3e9"
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    "kind": "arxiv",
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}