Pith Number

pith:2GCDGRS4

pith:2026:2GCDGRS4DE66FX25YYTNXZTLTC

not attested not anchored not stored refs resolved

Parallelizing Counterfactual Regret Minimization

Juho Kim, Tuomas Sandholm

Counterfactual regret minimization can be reframed as linear algebra operations to run up to four orders of magnitude faster on GPUs.

arxiv:2605.14277 v1 · 2026-05-14 · cs.AI · cs.GT

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2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications 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 present a generalized parallelization framework, reframing CFR as a series of linear algebra operations. ... our CFR implementation on a GPU is up to four orders of magnitude faster than Google DeepMind OpenSpiel's CFR implementations on a CPU.

C2weakest assumption

That the linear-algebra reformulation of CFR exactly preserves the original regret bounds and convergence properties without introducing floating-point or parallelism-induced errors.

C3one line summary

Reframing CFR as linear algebra operations enables GPU parallelization with up to 10,000x speedup over standard CPU implementations.

References

37 extracted · 37 resolved · 0 Pith anchors

[1] G. E. Blelloch. Programming parallel algorithms.Commun. ACM, 39(3):85–97, 1996 1996

[2] N. Brown and T. Sandholm. Regret-based pruning in extensive-form games. InProceedings of the Annual Conference on Neural Information Processing Systems (NeurIPS), 2015 2015

[3] N. Brown and T. Sandholm. Reduced space and faster convergence in imperfect-information games via pruning. InProceedings of the International Conference on Machine Learning (ICML), 2017 2017

[4] N. Brown and T. Sandholm. Superhuman AI for heads-up no-limit poker: Libratus beats top professionals.Science, 359(6374):418–424, 2018 2018

[5] N. Brown and T. Sandholm. Superhuman AI for multiplayer poker.Science, 365(6456):885–890, 2019 2019

Receipt and verification

First computed	2026-05-17T23:39:10.326403Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d18433465c193de2df5dc626dbe66b988f82e0f19816a72f8e4fcbf56800a0b0

Aliases

arxiv: 2605.14277 · arxiv_version: 2605.14277v1 · doi: 10.48550/arxiv.2605.14277 · pith_short_12: 2GCDGRS4DE66 · pith_short_16: 2GCDGRS4DE66FX25 · pith_short_8: 2GCDGRS4

Agent API

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/2GCDGRS4DE66FX25YYTNXZTLTC \
  | 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: d18433465c193de2df5dc626dbe66b988f82e0f19816a72f8e4fcbf56800a0b0

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "cd93e7940ddcd3129242c938329234a37819e400343a83a442a85a4cf1e8ba00",
    "cross_cats_sorted": [
      "cs.GT"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "cs.AI",
    "submitted_at": "2026-05-14T02:22:27Z",
    "title_canon_sha256": "06dc76c3524195e86b9d7082d0afd1bed7dd246c2148d53d14663494659907dd"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.14277",
    "kind": "arxiv",
    "version": 1
  }
}