Pith Number

pith:GJY3DGIE

pith:2026:GJY3DGIEWTMINUOY2YSHWGK4WK

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Entropy Regularization under Bayesian Drift Uncertainty

Andy Au

Gaussian policies remain optimal for entropy-regularized mean-variance optimization under Bayesian drift uncertainty, yielding closed-form belief-dependent solutions.

arxiv:2602.16862 v3 · 2026-02-18 · math.OC · q-fin.PM

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Claims

C1strongest claim

Gaussian policies remain optimal under partial information, the value function is quadratic in wealth, and belief-dependent coefficients admit closed-form solutions. The mean control is identical to deterministic Bayesian Markowitz feedback; entropy regularization affects only the policy variance. Notably, optimal policy variance increases with posterior conviction |m_t|.

C2weakest assumption

The model permits closed-form solutions under the combination of linear-Gaussian dynamics, quadratic costs, and Bayesian updating of the drift, which may not generalize if the uncertainty structure or cost functions deviate from these standard forms.

C3one line summary

Under Bayesian drift uncertainty, entropy regularization leaves mean control identical to deterministic Bayesian Markowitz while making optimal policy variance increase with posterior conviction |m_t| for added robustness without affecting information gain.

Formal links

3 machine-checked theorem links

Receipt and verification

First computed	2026-06-09T02:07:21.656068Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3271b19904b4d886d1d8d6247b195cb2a2bde62a93fbdb08a4b9d8139bd9330d

Aliases

arxiv: 2602.16862 · arxiv_version: 2602.16862v3 · doi: 10.48550/arxiv.2602.16862 · pith_short_12: GJY3DGIEWTMI · pith_short_16: GJY3DGIEWTMINUOY · pith_short_8: GJY3DGIE

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/GJY3DGIEWTMINUOY2YSHWGK4WK \
  | 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: 3271b19904b4d886d1d8d6247b195cb2a2bde62a93fbdb08a4b9d8139bd9330d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c704e25e98fc7d239be9d202cec5528ac1c5a5dea01aaf73e1af7d5356f077ef",
    "cross_cats_sorted": [
      "q-fin.PM"
    ],
    "license": "http://creativecommons.org/licenses/by-sa/4.0/",
    "primary_cat": "math.OC",
    "submitted_at": "2026-02-18T20:42:32Z",
    "title_canon_sha256": "4e3967aea91b86bd0f8d7e0753273ab7b79f55616896a035de83cb207d8f29ca"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2602.16862",
    "kind": "arxiv",
    "version": 3
  }
}