Pith Number

pith:7BXAU7YP

pith:2026:7BXAU7YPLUWRXTYB5P3WGRFDEV

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On Gaussian approximation for entropy-regularized Q-learning with function approximation

Alexey Naumov, Artemy Rubtsov, Eric Moulines, Rahul Singh, Sergey Samsonov

Entropy-regularized Q-learning with linear function approximation yields a Gaussian approximation bound of order n to the minus one-fourth for Polyak-Ruppert averaged iterates.

arxiv:2605.17678 v1 · 2026-05-17 · stat.ML · cs.LG

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\pithnumber{7BXAU7YPLUWRXTYB5P3WGRFDEV}

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Claims

C1strongest claim

We establish a Gaussian approximation bound in the convex distance with rate of order n^{-1/4}, up to polylogarithmic factors in n, for the Polyak-Ruppert averaged iterates.

C2weakest assumption

The sequence of observed triples (s_k, a_k, s_{k+1}) forms a uniformly geometrically ergodic Markov chain, together with suitable regularity conditions for the projected soft Bellman equation.

C3one line summary

Establishes n^{-1/4} Gaussian approximation in convex distance for averaged entropy-regularized Q-learning with linear function approximation and polynomial stepsizes.

References

40 extracted · 40 resolved · 3 Pith anchors

[1] Residual algorithms: Reinforcement learning with function approximation 1995

[2] The reverse isoperimetric problem for gaussian measure.Discrete & Computational Geometry, 10(4):411–420, 1993 1993

[3] Bertsekas and John N 1996

[4] Gaussian approximation for two-timescale linear stochastic approximation 2026

[5] Finite-sample analysis of nonlinear stochastic approximation with applications in reinforcement learning.Automatica, 146:110623, 2022 2022

Receipt and verification

First computed	2026-05-20T00:04:52.300419Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f86e0a7f0f5d2d1bcf01ebf76344a3256edac56fc99daef1829bc0016618f5a9

Aliases

arxiv: 2605.17678 · arxiv_version: 2605.17678v1 · doi: 10.48550/arxiv.2605.17678 · pith_short_12: 7BXAU7YPLUWR · pith_short_16: 7BXAU7YPLUWRXTYB · pith_short_8: 7BXAU7YP

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/7BXAU7YPLUWRXTYB5P3WGRFDEV \
  | 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: f86e0a7f0f5d2d1bcf01ebf76344a3256edac56fc99daef1829bc0016618f5a9

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "305751d645b8169b31a068444e82fb41a3ed378b60a9bc5ae42b6d0c994f3642",
    "cross_cats_sorted": [
      "cs.LG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "stat.ML",
    "submitted_at": "2026-05-17T22:23:25Z",
    "title_canon_sha256": "f8d624e8e6a49e2ee9564ecac766377ee3c3d9631205e613db9d7bb93bc7a742"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.17678",
    "kind": "arxiv",
    "version": 1
  }
}