Pith Number

pith:N4F3NZQV

pith:2026:N4F3NZQVOSVOSQXFHE4IZIZAXE

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Misspecified Universal Learning

Meir Feder, Shlomi Vituri

Misspecified universal learning with log-loss admits an optimal learner derived from minimax regret analysis.

arxiv:2605.10282 v2 · 2026-05-11 · cs.IT · math.IT

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\pithnumber{N4F3NZQVOSVOSQXFHE4IZIZAXE}

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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

We analyze the minimax regret in the misspecified setting and derive the corresponding optimal universal learner. We propose this formulation as a unified framework for universal learning, applicable to any form of uncertainty in the data-generating process, across both online and batch data arrival modes, as well as supervised and unsupervised learning tasks.

C2weakest assumption

That the minimax regret analysis and optimal learner derivation from the well-specified case extend directly to the misspecified case Φ ⊃ Θ without introducing new technical obstacles or requiring additional assumptions on the relationship between Θ and Φ.

C3one line summary

Minimax regret is characterized for misspecified universal learning with log-loss, yielding the optimal universal learner as a unified framework for any uncertainty in the data-generating process.

Receipt and verification

First computed	2026-06-02T03:04:41.953126Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6f0bb6e61574aae942e539388ca320b91a192092acaaa326b085002a1b600e2a

Aliases

arxiv: 2605.10282 · arxiv_version: 2605.10282v2 · doi: 10.48550/arxiv.2605.10282 · pith_short_12: N4F3NZQVOSVO · pith_short_16: N4F3NZQVOSVOSQXF · pith_short_8: N4F3NZQV

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/N4F3NZQVOSVOSQXFHE4IZIZAXE \
  | 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: 6f0bb6e61574aae942e539388ca320b91a192092acaaa326b085002a1b600e2a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "874afd35b23b33a17ae1b03cd6acae967942e57ebb3410f1d8e4891dd6fadf9a",
    "cross_cats_sorted": [
      "math.IT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.IT",
    "submitted_at": "2026-05-11T09:44:02Z",
    "title_canon_sha256": "cb30071320da0b596f3043e477f8defffe786c2574ef374546e9e92848fc3ae2"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.10282",
    "kind": "arxiv",
    "version": 2
  }
}