Pith Number

pith:IBOON75N

pith:2026:IBOON75NXU35CHZHNVCJSICENA

not attested not anchored not stored refs pending

Cost-Aware Learning

Amir Globerson, Clara Mohri, Haim Kaplan, Tomer Koren, Yishay Mansour

By accounting for different sampling costs, cost-aware stochastic gradient descent reaches target accuracy at lower total cost and reduces token usage by up to 30 percent in LLM policy optimization.

arxiv:2604.28020 v2 · 2026-04-30 · cs.LG

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\pithnumber{IBOON75NXU35CHZHNVCJSICENA}

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Record completeness

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2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

✓ Portable graph bundle live · download bundle · merged state

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

Empirical results on 1.5B and 8B LLMs demonstrate that our approach reduces the tokens used in policy optimization by up to about 30% while matching or exceeding baseline accuracy.

C2weakest assumption

The per-component sampling costs are known in advance and can be used to set sampling probabilities without introducing bias that harms convergence; this is stated implicitly in the cost-aware SGD derivation and the GRPO adaptation.

C3one line summary

Cost-aware SGD achieves target error with lower total sampling cost than standard methods, and Cost-Aware GRPO reduces token usage by up to 30% in LLM reinforcement learning while matching baseline performance.

Receipt and verification

First computed	2026-06-01T02:03:42.199752Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

405ce6ffadbd37d11f276d449920446828560d01b951f46c8598b9f01d0b33aa

Aliases

arxiv: 2604.28020 · arxiv_version: 2604.28020v2 · doi: 10.48550/arxiv.2604.28020 · pith_short_12: IBOON75NXU35 · pith_short_16: IBOON75NXU35CHZH · pith_short_8: IBOON75N

Agent API

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/IBOON75NXU35CHZHNVCJSICENA \
  | 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: 405ce6ffadbd37d11f276d449920446828560d01b951f46c8598b9f01d0b33aa

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e203bea884ca6872e40e862b8e31299cd16b3707afb0f879b35534da2de819c6",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "cs.LG",
    "submitted_at": "2026-04-30T15:39:09Z",
    "title_canon_sha256": "ceb970895d645166143f06e611672c4dc852112665822d98373e8c5c76a46a20"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2604.28020",
    "kind": "arxiv",
    "version": 2
  }
}