Pith Number

pith:AEK7UWYQ

pith:2026:AEK7UWYQXAQCT5OV7EZDLNOFXY

not attested not anchored not stored refs resolved

Stochastic Zeroth-Order Optimization Under Heavy-Tailed Noise

El Mahdi Chayti, Imane Rahali, Omar Saadi, Qiuyi Zhang, Taha El Bakkali

Clipped scalar directional estimates let zeroth-order methods find stationary points under heavy-tailed noise with near-optimal query rates.

arxiv:2605.17394 v1 · 2026-05-17 · math.OC

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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

Under sample-wise smoothness and a weak-L_p tail condition on sample-gradient noise, RSC-ZO finds an ε-stationary point with high probability using Õ(d^{p/2(p-1)} ε^{-(3p-2)/(p-1)}) noisy function evaluations.

C2weakest assumption

That weak-L_p control of the sample gradient noise can be transferred to the scalar directional finite-difference estimates without additional assumptions that would invalidate the high-probability bound (abstract states this transfer is nontrivial and is the key technical step).

C3one line summary

RSC-ZO achieves high-probability ε-stationary points for stochastic ZO optimization under weak-L_p heavy-tailed noise with Õ(d^{p/2(p-1)} ε^{-(3p-2)/(p-1)}) function queries.

References

41 extracted · 41 resolved · 2 Pith anchors

[1] SIAM journal on optimization , volume= 2013

[2] Proceedings of The 28th International Conference on Artificial Intelligence and Statistics , pages = 2025

[3] Foundations of Computational Mathematics , volume = 2017

[4] and Jordan, Michael I 2015

[5] Proceedings of the 10th ACM Workshop on Artificial Intelligence and Security (AISec) , pages =

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-20T00:03:56.299172Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0115fa5b10b82029f5d5f93235b5c5be08e0ed53946f2b85378782343a2548b8

Aliases

arxiv: 2605.17394 · arxiv_version: 2605.17394v1 · doi: 10.48550/arxiv.2605.17394 · pith_short_12: AEK7UWYQXAQC · pith_short_16: AEK7UWYQXAQCT5OV · pith_short_8: AEK7UWYQ

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/AEK7UWYQXAQCT5OV7EZDLNOFXY \
  | 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: 0115fa5b10b82029f5d5f93235b5c5be08e0ed53946f2b85378782343a2548b8

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "901177a23b4dcd697e0e5e02cb4147fa6f2b725af9d909adca26e8f5592f0ea5",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.OC",
    "submitted_at": "2026-05-17T11:24:17Z",
    "title_canon_sha256": "b5ecd8cfb048786c17c6cd98dc6b729c7b3a6cef93456709ccdff900e69a8b7e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.17394",
    "kind": "arxiv",
    "version": 1
  }
}