Pith Number

pith:3JOTCEYR

pith:2026:3JOTCEYRCH3ROJBNSXYBWFOHS7

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Unified High-Probability Analysis of Stochastic Variance-Reduced Estimation

Abolfazl Hashemi, Antesh Upadhyay, Anuran Makur, M. Berk Sahin, Sang Bin Moon, Zhankun Luo

A unified recursion with memory, reset, and correction terms yields high-probability bounds for variance-reduced stochastic estimators in normed spaces.

arxiv:2605.15388 v1 · 2026-05-14 · cs.LG

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Claims

C1strongest claim

Our main result is a unified high-probability bound proved using a new dimension-free vector-valued Freedman inequality, valid for smooth normed spaces involving random sums of vector martingales. ... We also derive the first Õ(ε^{-3}) oracle-complexity bounds for stochastic optimization with expectation constraints, improving upon the existing Õ(ε^{-4}) complexity.

C2weakest assumption

The central high-probability bound and complexity results rest on the validity and applicability of the newly introduced dimension-free vector-valued Freedman inequality in smooth normed spaces (including Banach spaces for mirror descent).

C3one line summary

A unified recursion framework for stochastic variance-reduced estimation yields high-probability bounds and the first Õ(ε^{-3}) oracle complexity for stochastic optimization with expectation constraints.

References

155 extracted · 155 resolved · 6 Pith anchors

[1] Global update tracking: A decentralized learning algorithm for heterogeneous data.Advances in neural information processing systems, 36:48939–48961, 2023 2023

[2] Towards weaker variance assumptions for stochastic optimization.arXiv preprint arXiv:2504.09951, 2025 2025

[3] On modification of an adaptive stochastic mirror descent algorithm for convex opti- mization problems with functional constraints 2020

[4] Neon2: Finding local minima via first-order oracles 2018

[5] Springer, Cham, Switzerland, second edition, 2021 2021

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-20T00:00:55.978991Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

da5d31131111f717242d95f01b15c797ec3a4b6474343c85cf6328b0053ca916

Aliases

arxiv: 2605.15388 · arxiv_version: 2605.15388v1 · doi: 10.48550/arxiv.2605.15388 · pith_short_12: 3JOTCEYRCH3R · pith_short_16: 3JOTCEYRCH3ROJBN · pith_short_8: 3JOTCEYR

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/3JOTCEYRCH3ROJBNSXYBWFOHS7 \
  | 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: da5d31131111f717242d95f01b15c797ec3a4b6474343c85cf6328b0053ca916

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a1ac0cb28bf02ba75c689f94a4ecd5aeb374185c767f227400b30536275fc0c5",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "cs.LG",
    "submitted_at": "2026-05-14T20:17:10Z",
    "title_canon_sha256": "2f0048b8781c6330df2e1c46100031bd7ac63e506a8724e6e39310b2ee34a842"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.15388",
    "kind": "arxiv",
    "version": 1
  }
}